Precalculus Examples

$2 x - 2 y + 3 z = 2$ , $(a + 3) x + (a - 3) y + z = 4$ , $3 x + 2 y - z = 1$

Step 1

Solve the equation for $x$ .

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Step 1.1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1.1

Add $2 y$ to both sides of the equation.

$2 x + 3 z = 2 + 2 y$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.1.2

Subtract $3 z$ from both sides of the equation.

$2 x = 2 + 2 y - 3 z$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$2 x = 2 + 2 y - 3 z$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2

Divide each term in $2 x = 2 + 2 y - 3 z$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = 2 + 2 y - 3 z$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2} + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2} + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{2} + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = \frac{2}{2} + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = \frac{2}{2} + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $2$ by $2$ .

$x = 1 + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2.3.1.2

Cancel the common factor of $2$ .

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Step 1.2.3.1.2.1

Cancel the common factor.

$x = 1 + \frac{2 y}{2} + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2.3.1.2.2

Divide $y$ by $1$ .

$x = 1 + y + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = 1 + y + \frac{- 3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = 1 + y - \frac{3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = 1 + y - \frac{3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = 1 + y - \frac{3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = 1 + y - \frac{3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

$x = 1 + y - \frac{3 z}{2}$

$(a + 3) x + (a - 3) y + z = 4$

$3 x + 2 y - z = 1$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $(a + 3) (1 + y - \frac{3 z}{2}) + (a - 3) \cdot y + z$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Expand $(a + 3) (1 + y - \frac{3 z}{2})$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot 1 + a y + a (- \frac{3 z}{2}) + 3 \cdot 1 + 3 y + 3 (- \frac{3 z}{2}) + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Multiply $a$ by $1$ .

$a + a y + a (- \frac{3 z}{2}) + 3 \cdot 1 + 3 y + 3 (- \frac{3 z}{2}) + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.2

Rewrite using the commutative property of multiplication.

$a + a y - a \frac{3 z}{2} + 3 \cdot 1 + 3 y + 3 (- \frac{3 z}{2}) + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.3

Combine $\frac{3 z}{2}$ and $a$ .

$a + a y - \frac{3 z a}{2} + 3 \cdot 1 + 3 y + 3 (- \frac{3 z}{2}) + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.4

Multiply $3$ by $1$ .

$a + a y - \frac{3 z a}{2} + 3 + 3 y + 3 (- \frac{3 z}{2}) + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.5

Multiply $3 (- \frac{3 z}{2})$ .

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Step 2.1.1.2.5.1

Multiply $- 1$ by $3$ .

$a + a y - \frac{3 z a}{2} + 3 + 3 y - 3 \frac{3 z}{2} + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.5.2

Combine $- 3$ and $\frac{3 z}{2}$ .

$a + a y - \frac{3 z a}{2} + 3 + 3 y + \frac{- 3 (3 z)}{2} + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.5.3

Multiply $3$ by $- 3$ .

$a + a y - \frac{3 z a}{2} + 3 + 3 y + \frac{- 9 z}{2} + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + a y - \frac{3 z a}{2} + 3 + 3 y + \frac{- 9 z}{2} + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.2.6

Move the negative in front of the fraction.

$a + a y - \frac{3 z a}{2} + 3 + 3 y - \frac{9 z}{2} + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + a y - \frac{3 z a}{2} + 3 + 3 y - \frac{9 z}{2} + (a - 3) \cdot y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.1.3

Apply the distributive property.

$a + a y - \frac{3 z a}{2} + 3 + 3 y - \frac{9 z}{2} + a y - 3 y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + a y - \frac{3 z a}{2} + 3 + 3 y - \frac{9 z}{2} + a y - 3 y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.2

Simplify by adding terms.

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Step 2.1.2.1

Combine the opposite terms in $a + a y - \frac{3 z a}{2} + 3 + 3 y - \frac{9 z}{2} + a y - 3 y + z$ .

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Step 2.1.2.1.1

Subtract $3 y$ from $3 y$ .

$a + a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + a y + 0 + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.2.1.2

Add $a + a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + a y$ and $0$ .

$a + a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + a y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + a y + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.2.2

Add $a y$ and $a y$ .

$a + 2 a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + 2 a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + z = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.3

To write $z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a + 2 a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + z \cdot \frac{2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.4

Simplify terms.

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Step 2.1.4.1

Combine $z$ and $\frac{2}{2}$ .

$a + 2 a y - \frac{3 z a}{2} + 3 - \frac{9 z}{2} + \frac{z \cdot 2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.4.2

Combine the numerators over the common denominator.

$a + 2 a y - \frac{3 z a}{2} + 3 + \frac{- 9 z + z \cdot 2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.4.3

Combine the numerators over the common denominator.

$a + 2 a y + 3 + \frac{- 3 z a - 9 z + z \cdot 2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + 2 a y + 3 + \frac{- 3 z a - 9 z + z \cdot 2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.5

Move $2$ to the left of $z$ .

$a + 2 a y + 3 + \frac{- 3 z a - 9 z + 2 z}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.6

Simplify terms.

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Step 2.1.6.1

Add $- 9 z$ and $2 z$ .

$a + 2 a y + 3 + \frac{- 3 z a - 7 z}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.6.2

Factor $z$ out of $- 3 z a - 7 z$ .

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Step 2.1.6.2.1

Factor $z$ out of $- 3 z a$ .

$a + 2 a y + 3 + \frac{z (- 3 a) - 7 z}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.6.2.2

Factor $z$ out of $- 7 z$ .

$a + 2 a y + 3 + \frac{z (- 3 a) + z \cdot - 7}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.6.2.3

Factor $z$ out of $z (- 3 a) + z \cdot - 7$ .

$a + 2 a y + 3 + \frac{z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + 2 a y + 3 + \frac{z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$a + 2 a y + 3 + \frac{z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.7

To write $a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 a y + 3 + a \cdot \frac{2}{2} + \frac{z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.8

Simplify terms.

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Step 2.1.8.1

Combine $a$ and $\frac{2}{2}$ .

$2 a y + 3 + \frac{a \cdot 2}{2} + \frac{z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.8.2

Combine the numerators over the common denominator.

$2 a y + 3 + \frac{a \cdot 2 + z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$2 a y + 3 + \frac{a \cdot 2 + z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.9

Simplify the numerator.

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Step 2.1.9.1

Move $2$ to the left of $a$ .

$2 a y + 3 + \frac{2 \cdot a + z (- 3 a - 7)}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.9.2

Apply the distributive property.

$2 a y + 3 + \frac{2 a + z (- 3 a) + z \cdot - 7}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.9.3

Rewrite using the commutative property of multiplication.

$2 a y + 3 + \frac{2 a - 3 z a + z \cdot - 7}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.9.4

Move $- 7$ to the left of $z$ .

$2 a y + 3 + \frac{2 a - 3 z a - 7 z}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$2 a y + 3 + \frac{2 a - 3 z a - 7 z}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.10

To write $2 a y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 a y \cdot \frac{2}{2} + \frac{2 a - 3 z a - 7 z}{2} + 3 = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.11

Simplify terms.

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Step 2.1.11.1

Combine $2 a y$ and $\frac{2}{2}$ .

$\frac{2 a y \cdot 2}{2} + \frac{2 a - 3 z a - 7 z}{2} + 3 = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.11.2

Combine the numerators over the common denominator.

$\frac{2 a y \cdot 2 + 2 a - 3 z a - 7 z}{2} + 3 = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$\frac{2 a y \cdot 2 + 2 a - 3 z a - 7 z}{2} + 3 = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.12

Multiply $2$ by $2$ .

$\frac{4 a y + 2 a - 3 z a - 7 z}{2} + 3 = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.13

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 a y + 2 a - 3 z a - 7 z}{2} + 3 \cdot \frac{2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.14

Combine $3$ and $\frac{2}{2}$ .

$\frac{4 a y + 2 a - 3 z a - 7 z}{2} + \frac{3 \cdot 2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.15

Combine the numerators over the common denominator.

$\frac{4 a y + 2 a - 3 z a - 7 z + 3 \cdot 2}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.1.16

Multiply $3$ by $2$ .

$\frac{4 a y + 2 a - 3 z a - 7 z + 6}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$\frac{4 a y + 2 a - 3 z a - 7 z + 6}{2} = 4$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.2

Multiply both sides by $2$ .

$\frac{4 a y + 2 a - 3 z a - 7 z + 6}{2} \cdot 2 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $\frac{4 a y + 2 a - 3 z a - 7 z + 6}{2} \cdot 2$ .

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Step 2.3.1.1.1

Cancel the common factor of $2$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

$\frac{4 a y + 2 a - 3 z a - 7 z + 6}{2} \cdot 2 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.3.1.1.1.2

Rewrite the expression.

$4 a y + 2 a - 3 z a - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y + 2 a - 3 z a - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.3.1.1.2

Reorder.

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Step 2.3.1.1.2.1

Move $z$ .

$4 a y + 2 a - 3 a z - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.3.1.1.2.2

Move $2 a$ .

$4 a y - 3 a z + 2 a - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y - 3 a z + 2 a - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y - 3 a z + 2 a - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y - 3 a z + 2 a - 7 z + 6 = 4 \cdot 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $4$ by $2$ .

$4 a y - 3 a z + 2 a - 7 z + 6 = 8$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y - 3 a z + 2 a - 7 z + 6 = 8$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y - 3 a z + 2 a - 7 z + 6 = 8$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4

Solve for $y$ .

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Step 2.4.1

Move all terms not containing $y$ to the right side of the equation.

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Step 2.4.1.1

Add $3 a z$ to both sides of the equation.

$4 a y + 2 a - 7 z + 6 = 8 + 3 a z$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.1.2

Subtract $2 a$ from both sides of the equation.

$4 a y - 7 z + 6 = 8 + 3 a z - 2 a$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.1.3

Add $7 z$ to both sides of the equation.

$4 a y + 6 = 8 + 3 a z - 2 a + 7 z$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.1.4

Subtract $6$ from both sides of the equation.

$4 a y = 8 + 3 a z - 2 a + 7 z - 6$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.1.5

Subtract $6$ from $8$ .

$4 a y = 3 a z - 2 a + 7 z + 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$4 a y = 3 a z - 2 a + 7 z + 2$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2

Divide each term in $4 a y = 3 a z - 2 a + 7 z + 2$ by $4 a$ and simplify.

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Step 2.4.2.1

Divide each term in $4 a y = 3 a z - 2 a + 7 z + 2$ by $4 a$ .

$\frac{4 a y}{4 a} = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $4$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{4 a y}{4 a} = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.2.1.2

Rewrite the expression.

$\frac{a y}{a} = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$\frac{a y}{a} = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.2.2

Cancel the common factor of $a$ .

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Step 2.4.2.2.2.1

Cancel the common factor.

$\frac{a y}{a} = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.2.2.2

Divide $y$ by $1$ .

$y = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Simplify each term.

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Step 2.4.2.3.1.1

Cancel the common factor of $a$ .

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Step 2.4.2.3.1.1.1

Cancel the common factor.

$y = \frac{3 a z}{4 a} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.1.2

Rewrite the expression.

$y = \frac{3 z}{4} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} + \frac{- 2 a}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.2

Cancel the common factor of $- 2$ and $4$ .

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Step 2.4.2.3.1.2.1

Factor $2$ out of $- 2 a$ .

$y = \frac{3 z}{4} + \frac{2 (- a)}{4 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.2.2

Cancel the common factors.

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Step 2.4.2.3.1.2.2.1

Factor $2$ out of $4 a$ .

$y = \frac{3 z}{4} + \frac{2 (- a)}{2 (2 a)} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{3 z}{4} + \frac{2 (- a)}{2 (2 a)} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{3 z}{4} + \frac{- a}{2 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} + \frac{- a}{2 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} + \frac{- a}{2 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.3

Cancel the common factor of $a$ .

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Step 2.4.2.3.1.3.1

Cancel the common factor.

$y = \frac{3 z}{4} + \frac{- a}{2 a} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.3.2

Rewrite the expression.

$y = \frac{3 z}{4} + \frac{- 1}{2} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} + \frac{- 1}{2} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.4

Move the negative in front of the fraction.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{2}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.5

Cancel the common factor of $2$ and $4$ .

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Step 2.4.2.3.1.5.1

Factor $2$ out of $2$ .

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{2 (1)}{4 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.5.2

Cancel the common factors.

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Step 2.4.2.3.1.5.2.1

Factor $2$ out of $4 a$ .

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{2 (1)}{2 (2 a)}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.5.2.2

Cancel the common factor.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{2 \cdot 1}{2 (2 a)}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 2.4.2.3.1.5.2.3

Rewrite the expression.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 x + 2 y - z = 1$

Step 3

Solve the equation for $z$ .

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Step 3.1

Simplify $3 (1 + \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} - \frac{3 z}{2}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Write $1$ as a fraction with a common denominator.

$3 (\frac{3 z}{4} + \frac{2}{2} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} - \frac{3 z}{2}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.2

Combine the numerators over the common denominator.

$3 (\frac{3 z}{4} + \frac{2 - 1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} - \frac{3 z}{2}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.3

Subtract $1$ from $2$ .

$3 (\frac{3 z}{4} + \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} - \frac{3 z}{2}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.4

To write $- \frac{3 z}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z}{4} - \frac{3 z}{2} \cdot \frac{2}{2}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.5

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.1.5.1

Multiply $\frac{3 z}{2}$ by $\frac{2}{2}$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z}{4} - \frac{3 z \cdot 2}{2 \cdot 2}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.5.2

Multiply $2$ by $2$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z}{4} - \frac{3 z \cdot 2}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z}{4} - \frac{3 z \cdot 2}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.6

Combine the numerators over the common denominator.

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z - 3 z \cdot 2}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7

Simplify each term.

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Step 3.1.1.7.1

Simplify the numerator.

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Step 3.1.1.7.1.1

Factor $3 z$ out of $3 z - 3 z \cdot 2$ .

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Step 3.1.1.7.1.1.1

Factor $3 z$ out of $3 z$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z (1) - 3 z \cdot 2}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7.1.1.2

Factor $3 z$ out of $- 3 z \cdot 2$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z (1) + 3 z (- 1 \cdot 2)}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7.1.1.3

Factor $3 z$ out of $3 z (1) + 3 z (- 1 \cdot 2)$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z (1 - 1 \cdot 2)}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z (1 - 1 \cdot 2)}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7.1.2

Multiply $- 1$ by $2$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z (1 - 2)}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7.1.3

Subtract $2$ from $1$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{3 z \cdot - 1}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7.1.4

Multiply $- 1$ by $3$ .

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{- 3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} + \frac{- 3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.7.2

Move the negative in front of the fraction.

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} - \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$3 (\frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a} - \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.8

Apply the distributive property.

$3 (\frac{1}{2}) + 3 (\frac{7 z}{4 a}) + 3 (\frac{1}{2 a}) + 3 (- \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9

Simplify.

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Step 3.1.1.9.1

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} + 3 (\frac{7 z}{4 a}) + 3 (\frac{1}{2 a}) + 3 (- \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9.2

Multiply $3 \frac{7 z}{4 a}$ .

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Step 3.1.1.9.2.1

Combine $3$ and $\frac{7 z}{4 a}$ .

$\frac{3}{2} + \frac{3 (7 z)}{4 a} + 3 (\frac{1}{2 a}) + 3 (- \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9.2.2

Multiply $7$ by $3$ .

$\frac{3}{2} + \frac{21 z}{4 a} + 3 (\frac{1}{2 a}) + 3 (- \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + 3 (\frac{1}{2 a}) + 3 (- \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9.3

Combine $3$ and $\frac{1}{2 a}$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} + 3 (- \frac{3 z}{4}) + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9.4

Multiply $3 (- \frac{3 z}{4})$ .

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Step 3.1.1.9.4.1

Multiply $- 1$ by $3$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - 3 \frac{3 z}{4} + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9.4.2

Combine $- 3$ and $\frac{3 z}{4}$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} + \frac{- 3 (3 z)}{4} + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.9.4.3

Multiply $3$ by $- 3$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} + \frac{- 9 z}{4} + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} + \frac{- 9 z}{4} + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} + \frac{- 9 z}{4} + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.10

Move the negative in front of the fraction.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + 2 (\frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.11

Apply the distributive property.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + 2 (\frac{3 z}{4}) + 2 (- \frac{1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12

Simplify.

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Step 3.1.1.12.1

Cancel the common factor of $2$ .

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Step 3.1.1.12.1.1

Factor $2$ out of $4$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + 2 (\frac{3 z}{2 (2)}) + 2 (- \frac{1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.1.2

Cancel the common factor.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + 2 (\frac{3 z}{2 \cdot 2}) + 2 (- \frac{1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.1.3

Rewrite the expression.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + 2 (- \frac{1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + 2 (- \frac{1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.2

Cancel the common factor of $2$ .

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Step 3.1.1.12.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + 2 (\frac{- 1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.2.2

Cancel the common factor.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + 2 (\frac{- 1}{2}) + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.2.3

Rewrite the expression.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + 2 (\frac{7 z}{4 a}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.3

Cancel the common factor of $2$ .

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Step 3.1.1.12.3.1

Factor $2$ out of $4 a$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + 2 (\frac{7 z}{2 (2 a)}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.3.2

Cancel the common factor.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + 2 (\frac{7 z}{2 (2 a)}) + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.3.3

Rewrite the expression.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.4

Cancel the common factor of $2$ .

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Step 3.1.1.12.4.1

Factor $2$ out of $2 a$ .

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + 2 (\frac{1}{2 (a)}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.4.2

Cancel the common factor.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + 2 (\frac{1}{2 a}) - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.1.12.4.3

Rewrite the expression.

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2} + \frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} - 1 + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{3}{2} - 1 \cdot \frac{2}{2} + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.3

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{3}{2} + \frac{- 1 \cdot 2}{2} + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{3 - 1 \cdot 2}{2} + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $- 1$ by $2$ .

$\frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{3 - 2}{2} + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.5.2

Subtract $2$ from $3$ .

$\frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{21 z}{4 a} + \frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z}{2 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.6

To write $\frac{7 z}{2 a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{21 z}{4 a} + \frac{7 z}{2 a} \cdot \frac{2}{2} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.7

Write each expression with a common denominator of $4 a$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.7.1

Multiply $\frac{7 z}{2 a}$ by $\frac{2}{2}$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{21 z}{4 a} + \frac{7 z \cdot 2}{2 a \cdot 2} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.7.2

Multiply $2$ by $2$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{21 z}{4 a} + \frac{7 z \cdot 2}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{21 z}{4 a} + \frac{7 z \cdot 2}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.8

Combine the numerators over the common denominator.

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{21 z + 7 z \cdot 2}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.9

Simplify the numerator.

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Step 3.1.9.1

Factor $7 z$ out of $21 z + 7 z \cdot 2$ .

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Step 3.1.9.1.1

Factor $7 z$ out of $21 z$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z (3) + 7 z \cdot 2}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.9.1.2

Factor $7 z$ out of $7 z \cdot 2$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z (3) + 7 z (2)}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.9.1.3

Factor $7 z$ out of $7 z (3) + 7 z (2)$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z (3 + 2)}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z (3 + 2)}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.9.2

Add $3$ and $2$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{7 z \cdot 5}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.9.3

Multiply $5$ by $7$ .

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} + \frac{1}{a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.10

To write $\frac{1}{a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{2 a} + \frac{1}{a} \cdot \frac{2}{2} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.11

Write each expression with a common denominator of $2 a$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.11.1

Multiply $\frac{1}{a}$ by $\frac{2}{2}$ .

$\frac{3}{2 a} + \frac{2}{a \cdot 2} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.11.2

Reorder the factors of $a \cdot 2$ .

$\frac{3}{2 a} + \frac{2}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{3}{2 a} + \frac{2}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.12

Combine the numerators over the common denominator.

$\frac{3 + 2}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.13

Add $3$ and $2$ .

$\frac{5}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.14

To write $\frac{3 z}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2 a} - \frac{9 z}{4} + \frac{3 z}{2} \cdot \frac{2}{2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.15

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.15.1

Multiply $\frac{3 z}{2}$ by $\frac{2}{2}$ .

$\frac{5}{2 a} - \frac{9 z}{4} + \frac{3 z \cdot 2}{2 \cdot 2} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.15.2

Multiply $2$ by $2$ .

$\frac{5}{2 a} - \frac{9 z}{4} + \frac{3 z \cdot 2}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} - \frac{9 z}{4} + \frac{3 z \cdot 2}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.16

Combine the numerators over the common denominator.

$\frac{5}{2 a} + \frac{- 9 z + 3 z \cdot 2}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.17

Simplify each term.

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Step 3.1.17.1

Simplify the numerator.

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Step 3.1.17.1.1

Factor $3 z$ out of $- 9 z + 3 z \cdot 2$ .

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Step 3.1.17.1.1.1

Factor $3 z$ out of $- 9 z$ .

$\frac{5}{2 a} + \frac{3 z (- 3) + 3 z \cdot 2}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.17.1.1.2

Factor $3 z$ out of $3 z \cdot 2$ .

$\frac{5}{2 a} + \frac{3 z (- 3) + 3 z (2)}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.17.1.1.3

Factor $3 z$ out of $3 z (- 3) + 3 z (2)$ .

$\frac{5}{2 a} + \frac{3 z (- 3 + 2)}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} + \frac{3 z (- 3 + 2)}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.17.1.2

Add $- 3$ and $2$ .

$\frac{5}{2 a} + \frac{3 z \cdot - 1}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.17.1.3

Multiply $- 1$ by $3$ .

$\frac{5}{2 a} + \frac{- 3 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} + \frac{- 3 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.17.2

Move the negative in front of the fraction.

$\frac{5}{2 a} - \frac{3 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} - \frac{3 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} - z = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.18

To write $- z$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{2 a} - \frac{3 z}{4} - z \cdot \frac{4}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.19

Simplify terms.

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Step 3.1.19.1

Combine $- z$ and $\frac{4}{4}$ .

$\frac{5}{2 a} - \frac{3 z}{4} + \frac{- z \cdot 4}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.19.2

Combine the numerators over the common denominator.

$\frac{5}{2 a} + \frac{- 3 z - z \cdot 4}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} + \frac{- 3 z - z \cdot 4}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20

Simplify each term.

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Step 3.1.20.1

Simplify the numerator.

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Step 3.1.20.1.1

Factor $z$ out of $- 3 z - z \cdot 4$ .

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Step 3.1.20.1.1.1

Factor $z$ out of $- 3 z$ .

$\frac{5}{2 a} + \frac{z \cdot - 3 - z \cdot 4}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20.1.1.2

Factor $z$ out of $- z \cdot 4$ .

$\frac{5}{2 a} + \frac{z \cdot - 3 + z (- 1 \cdot 4)}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20.1.1.3

Factor $z$ out of $z \cdot - 3 + z (- 1 \cdot 4)$ .

$\frac{5}{2 a} + \frac{z (- 3 - 1 \cdot 4)}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} + \frac{z (- 3 - 1 \cdot 4)}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20.1.2

Multiply $- 1$ by $4$ .

$\frac{5}{2 a} + \frac{z (- 3 - 4)}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20.1.3

Subtract $4$ from $- 3$ .

$\frac{5}{2 a} + \frac{z \cdot - 7}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} + \frac{z \cdot - 7}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20.2

Move $- 7$ to the left of $z$ .

$\frac{5}{2 a} + \frac{- 7 \cdot z}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.1.20.3

Move the negative in front of the fraction.

$\frac{5}{2 a} - \frac{7 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} - \frac{7 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{5}{2 a} - \frac{7 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2

Find the LCD of the terms in the equation.

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Step 3.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 a, 4, 2, 4 a, 1$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.2

Since $2 a, 4, 2, 4 a, 1$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $2, 4, 2, 4, 1$ then find LCM for the variable part $a^{1}, a^{1}$ .

Since $2 a, 4, 2, 4 a, 1$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $2, 4, 2, 4, 1$ then find LCM for the variable part a,a.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.3

The LCM is the smallest positive number that all of the numbers divide into evenly.

$1$ List the prime factors of each number.

$2$ Multiply each factor the greatest number of times it occurs in either number.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.4

Since $2$ has no factors besides $1$ and $2$ .

$2$ is a prime number

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.5

$4$ has factors of $2$ and $2$ .

$2 \cdot 2$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.6

Since $2$ has no factors besides $1$ and $2$ .

$2$ is a prime number

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.7

$4$ has factors of $2$ and $2$ .

$2 \cdot 2$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.8

The number $1$ is not a prime number because it only has one positive factor, which is itself.

Not prime

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.9

The LCM of $2, 4, 2, 4, 1$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.10

Multiply $2$ by $2$ .

$4$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.11

The factor for $a^{1}$ is $a$ itself.

$a = a$

a occurs $1$ time.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.12

The LCM of $a^{1}, a^{1}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.2.13

The LCM for $2 a, 4, 2, 4 a, 1$ is the numeric part $4$ multiplied by the variable part.

$4 a$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$4 a$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3

Multiply each term in $\frac{5}{2 a} - \frac{7 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$ by $4 a$ to eliminate the fractions.

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Step 3.3.1

Multiply each term in $\frac{5}{2 a} - \frac{7 z}{4} + \frac{1}{2} + \frac{35 z}{4 a} = 1$ by $4 a$ .

$\frac{5}{2 a} \cdot (4 a) - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Simplify each term.

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Step 3.3.2.1.1

Rewrite using the commutative property of multiplication.

$4 (\frac{5}{2 a}) \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.2

Cancel the common factor of $2$ .

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Step 3.3.2.1.2.1

Factor $2$ out of $4$ .

$2 (2) (\frac{5}{2 a}) \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.2.2

Factor $2$ out of $2 a$ .

$2 (2) (\frac{5}{2 (a)}) \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.2.3

Cancel the common factor.

$2 \cdot (2 (\frac{5}{2 a})) \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.2.4

Rewrite the expression.

$2 (\frac{5}{a}) \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$2 (\frac{5}{a}) \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.3

Combine $2$ and $\frac{5}{a}$ .

$\frac{2 \cdot 5}{a} \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.4

Multiply $2$ by $5$ .

$\frac{10}{a} \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.5

Cancel the common factor of $a$ .

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Step 3.3.2.1.5.1

Cancel the common factor.

$\frac{10}{a} \cdot a - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.5.2

Rewrite the expression.

$10 - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - \frac{7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.6

Cancel the common factor of $4$ .

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Step 3.3.2.1.6.1

Move the leading negative in $- \frac{7 z}{4}$ into the numerator.

$10 + \frac{- 7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.6.2

Factor $4$ out of $4 a$ .

$10 + \frac{- 7 z}{4} \cdot (4 (a)) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.6.3

Cancel the common factor.

$10 + \frac{- 7 z}{4} \cdot (4 a) + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.6.4

Rewrite the expression.

$10 - 7 z a + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + \frac{1}{2} \cdot (4 a) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.7

Cancel the common factor of $2$ .

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Step 3.3.2.1.7.1

Factor $2$ out of $4 a$ .

$10 - 7 z a + \frac{1}{2} \cdot (2 (2 a)) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.7.2

Cancel the common factor.

$10 - 7 z a + \frac{1}{2} \cdot (2 (2 a)) + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.7.3

Rewrite the expression.

$10 - 7 z a + 2 a + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + \frac{35 z}{4 a} \cdot (4 a) = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.8

Rewrite using the commutative property of multiplication.

$10 - 7 z a + 2 a + 4 (\frac{35 z}{4 a}) \cdot a = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.9

Cancel the common factor of $4$ .

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Step 3.3.2.1.9.1

Factor $4$ out of $4 a$ .

$10 - 7 z a + 2 a + 4 (\frac{35 z}{4 (a)}) \cdot a = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.9.2

Cancel the common factor.

$10 - 7 z a + 2 a + 4 (\frac{35 z}{4 a}) \cdot a = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.9.3

Rewrite the expression.

$10 - 7 z a + 2 a + \frac{35 z}{a} \cdot a = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + \frac{35 z}{a} \cdot a = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.10

Cancel the common factor of $a$ .

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Step 3.3.2.1.10.1

Cancel the common factor.

$10 - 7 z a + 2 a + \frac{35 z}{a} \cdot a = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.2.1.10.2

Rewrite the expression.

$10 - 7 z a + 2 a + 35 z = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + 35 z = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + 35 z = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + 35 z = 1 (4 a)$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply $4 a$ by $1$ .

$10 - 7 z a + 2 a + 35 z = 4 a$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + 35 z = 4 a$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$10 - 7 z a + 2 a + 35 z = 4 a$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4

Solve the equation.

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Step 3.4.1

Move all terms not containing $z$ to the right side of the equation.

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Step 3.4.1.1

Subtract $10$ from both sides of the equation.

$- 7 z a + 2 a + 35 z = 4 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.1.2

Subtract $2 a$ from both sides of the equation.

$- 7 z a + 35 z = 4 a - 10 - 2 a$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.1.3

Subtract $2 a$ from $4 a$ .

$- 7 z a + 35 z = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$- 7 z a + 35 z = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.2

Factor $7 z$ out of $- 7 z a + 35 z$ .

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Step 3.4.2.1

Factor $7 z$ out of $- 7 z a$ .

$7 z (- 1 a) + 35 z = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.2.2

Factor $7 z$ out of $35 z$ .

$7 z (- 1 a) + 7 z (5) = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.2.3

Factor $7 z$ out of $7 z (- 1 a) + 7 z (5)$ .

$7 z (- 1 a + 5) = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$7 z (- 1 a + 5) = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.3

Rewrite $- 1 a$ as $- a$ .

$7 z (- a + 5) = 2 a - 10$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.4

Divide each term in $7 z (- a + 5) = 2 a - 10$ by $7 (- a + 5)$ and simplify.

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Step 3.4.4.1

Divide each term in $7 z (- a + 5) = 2 a - 10$ by $7 (- a + 5)$ .

$\frac{7 z (- a + 5)}{7 (- a + 5)} = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.4.2

Simplify the left side.

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Step 3.4.4.2.1

Cancel the common factor of $7$ .

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Step 3.4.4.2.1.1

Cancel the common factor.

$\frac{7 z (- a + 5)}{7 (- a + 5)} = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.4.2.1.2

Rewrite the expression.

$\frac{z (- a + 5)}{- a + 5} = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$\frac{z (- a + 5)}{- a + 5} = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.4.2.2

Cancel the common factor of $- a + 5$ .

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Step 3.4.4.2.2.1

Cancel the common factor.

$\frac{z (- a + 5)}{- a + 5} = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.4.2.2.2

Divide $z$ by $1$ .

$z = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$z = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$z = \frac{2 a}{7 (- a + 5)} + \frac{- 10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 3.4.4.3

Simplify the right side.

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Step 3.4.4.3.1

Move the negative in front of the fraction.

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$y = \frac{3 z}{4} - \frac{1}{2} + \frac{7 z}{4 a} + \frac{1}{2 a}$

$x = 1 + y - \frac{3 z}{2}$

Step 4

Simplify the right side.

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Step 4.1

Simplify $\frac{3 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$ .

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Step 4.1.1

Simplify each term.

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Step 4.1.1.1

Simplify the numerator.

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Step 4.1.1.1.1

Combine the numerators over the common denominator.

$y = \frac{3 (\frac{2 a - 10}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.2

Factor $2$ out of $2 a - 10$ .

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Step 4.1.1.1.2.1

Factor $2$ out of $2 a$ .

$y = \frac{3 (\frac{2 (a) - 10}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.2.2

Factor $2$ out of $- 10$ .

$y = \frac{3 (\frac{2 a + 2 \cdot - 5}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.2.3

Factor $2$ out of $2 a + 2 \cdot - 5$ .

$y = \frac{3 (\frac{2 (a - 5)}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{3 (\frac{2 (a - 5)}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.3

Cancel the common factor of $a - 5$ and $- a + 5$ .

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Step 4.1.1.1.3.1

Factor $- 1$ out of $a$ .

$y = \frac{3 (\frac{2 (- 1 (- a) - 5)}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.3.2

Rewrite $- 5$ as $- 1 (5)$ .

$y = \frac{3 (\frac{2 (- 1 (- a) - 1 \cdot 5)}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.3.3

Factor $- 1$ out of $- 1 (- a) - 1 (5)$ .

$y = \frac{3 (\frac{2 (- 1 (- a + 5))}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.3.4

Cancel the common factor.

$y = \frac{3 (\frac{2 (- 1 (- a + 5))}{7 (- a + 5)})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.3.5

Rewrite the expression.

$y = \frac{3 (\frac{2 \cdot (- 1)}{7})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{3 (\frac{2 \cdot (- 1)}{7})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.4

Multiply $2$ by $- 1$ .

$y = \frac{3 (\frac{- 2}{7})}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.5

Move the negative in front of the fraction.

$y = \frac{3 \cdot (- 1 (\frac{2}{7}))}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.6

Combine exponents.

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Step 4.1.1.1.6.1

Factor out negative.

$y = \frac{- (3 (\frac{2}{7}))}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.6.2

Combine $3$ and $\frac{2}{7}$ .

$y = \frac{- \frac{3 \cdot 2}{7}}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.1.6.3

Multiply $3$ by $2$ .

$y = \frac{- \frac{6}{7}}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{- \frac{6}{7}}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{- \frac{6}{7}}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{6}{7} \cdot \frac{1}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.3.1

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$y = \frac{- 6}{7} \cdot \frac{1}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.3.2

Factor $2$ out of $- 6$ .

$y = \frac{2 (- 3)}{7} \cdot \frac{1}{4} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.3.3

Factor $2$ out of $4$ .

$y = \frac{2 \cdot - 3}{7} \cdot \frac{1}{2 \cdot 2} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.3.4

Cancel the common factor.

$y = \frac{2 \cdot - 3}{7} \cdot \frac{1}{2 \cdot 2} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.3.5

Rewrite the expression.

$y = \frac{- 3}{7} \cdot \frac{1}{2} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{- 3}{7} \cdot \frac{1}{2} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.4

Multiply $\frac{- 3}{7}$ by $\frac{1}{2}$ .

$y = \frac{- 3}{7 \cdot 2} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.5

Multiply $7$ by $2$ .

$y = \frac{- 3}{14} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.6

Move the negative in front of the fraction.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7

Simplify the numerator.

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Step 4.1.1.7.1

Combine the numerators over the common denominator.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 a - 10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.2

Factor $2$ out of $2 a - 10$ .

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Step 4.1.1.7.2.1

Factor $2$ out of $2 a$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (a) - 10}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.2.2

Factor $2$ out of $- 10$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 a + 2 \cdot - 5}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.2.3

Factor $2$ out of $2 a + 2 \cdot - 5$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (a - 5)}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (a - 5)}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.3

Cancel the common factor of $a - 5$ and $- a + 5$ .

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Step 4.1.1.7.3.1

Factor $- 1$ out of $a$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (- 1 (- a) - 5)}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.3.2

Rewrite $- 5$ as $- 1 (5)$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (- 1 (- a) - 1 \cdot 5)}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.3.3

Factor $- 1$ out of $- 1 (- a) - 1 (5)$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (- 1 (- a + 5))}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.3.4

Cancel the common factor.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 (- 1 (- a + 5))}{7 (- a + 5)})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.3.5

Rewrite the expression.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 \cdot (- 1)}{7})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{2 \cdot (- 1)}{7})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.4

Multiply $2$ by $- 1$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 (\frac{- 2}{7})}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.5

Move the negative in front of the fraction.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{7 \cdot (- 1 (\frac{2}{7}))}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.6

Combine exponents.

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Step 4.1.1.7.6.1

Factor out negative.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- (7 (\frac{2}{7}))}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.6.2

Combine $7$ and $\frac{2}{7}$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- \frac{7 \cdot 2}{7}}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.6.3

Multiply $7$ by $2$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- \frac{14}{7}}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- \frac{14}{7}}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.7.7

Divide $14$ by $7$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- 1 \cdot 2}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- 1 \cdot 2}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.8

Multiply $- 1$ by $2$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- 2}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.9

Cancel the common factor of $- 2$ and $4$ .

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Step 4.1.1.9.1

Factor $2$ out of $- 2$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{2 (- 1)}{4 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.9.2

Cancel the common factors.

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Step 4.1.1.9.2.1

Factor $2$ out of $4 a$ .

$y = - \frac{3}{14} - \frac{1}{2} + \frac{2 (- 1)}{2 (2 a)} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.9.2.2

Cancel the common factor.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{2 \cdot - 1}{2 (2 a)} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.9.2.3

Rewrite the expression.

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- 1}{2 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- 1}{2 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} + \frac{- 1}{2 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.1.10

Move the negative in front of the fraction.

$y = - \frac{3}{14} - \frac{1}{2} - \frac{1}{2 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2} - \frac{1}{2 a} + \frac{1}{2 a}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.2

Combine the opposite terms in $- \frac{3}{14} - \frac{1}{2} - \frac{1}{2 a} + \frac{1}{2 a}$ .

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Step 4.1.2.1

Add $- \frac{1}{2 a}$ and $\frac{1}{2 a}$ .

$y = - \frac{3}{14} - \frac{1}{2} + 0$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.2.2

Add $- \frac{3}{14} - \frac{1}{2}$ and $0$ .

$y = - \frac{3}{14} - \frac{1}{2}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{1}{2}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{3}{14} - \frac{1}{2} \cdot \frac{7}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1.4.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$y = - \frac{3}{14} - \frac{7}{2 \cdot 7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.4.2

Multiply $2$ by $7$ .

$y = - \frac{3}{14} - \frac{7}{14}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{3}{14} - \frac{7}{14}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.5

Simplify the expression.

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Step 4.1.5.1

Combine the numerators over the common denominator.

$y = \frac{- 3 - 7}{14}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.5.2

Subtract $7$ from $- 3$ .

$y = \frac{- 10}{14}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{- 10}{14}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.6

Cancel the common factor of $- 10$ and $14$ .

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Step 4.1.6.1

Factor $2$ out of $- 10$ .

$y = \frac{2 (- 5)}{14}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.6.2

Cancel the common factors.

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Step 4.1.6.2.1

Factor $2$ out of $14$ .

$y = \frac{2 \cdot - 5}{2 \cdot 7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.6.2.2

Cancel the common factor.

$y = \frac{2 \cdot - 5}{2 \cdot 7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.6.2.3

Rewrite the expression.

$y = \frac{- 5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{- 5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = \frac{- 5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 4.1.7

Move the negative in front of the fraction.

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 + y - \frac{3 z}{2}$

Step 5

Substitute the calculated values for $y, z$ into the equation for $x$ .

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Step 5.1

Simplify the left side.

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Step 5.1.1

Remove parentheses.

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $1 - \frac{5}{7} - \frac{3 (\frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)})}{2}$ .

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Step 5.2.1.1

Simplify each term.

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Step 5.2.1.1.1

Simplify the numerator.

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Step 5.2.1.1.1.1

Combine the numerators over the common denominator.

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 a - 10}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.2

Factor $2$ out of $2 a - 10$ .

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Step 5.2.1.1.1.2.1

Factor $2$ out of $2 a$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (a) - 10}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.2.2

Factor $2$ out of $- 10$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 a + 2 \cdot - 5}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.2.3

Factor $2$ out of $2 a + 2 \cdot - 5$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (a - 5)}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (a - 5)}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.3

Cancel the common factor of $a - 5$ and $- a + 5$ .

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Step 5.2.1.1.1.3.1

Factor $- 1$ out of $a$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (- 1 (- a) - 5)}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.3.2

Rewrite $- 5$ as $- 1 (5)$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (- 1 (- a) - 1 \cdot 5)}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.3.3

Factor $- 1$ out of $- 1 (- a) - 1 (5)$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (- 1 (- a + 5))}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.3.4

Cancel the common factor.

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 (- 1 (- a + 5))}{7 (- a + 5)})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.3.5

Rewrite the expression.

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 \cdot (- 1)}{7})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} - \frac{3 (\frac{2 \cdot (- 1)}{7})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.4

Multiply $2$ by $- 1$ .

$x = 1 - \frac{5}{7} - \frac{3 (\frac{- 2}{7})}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.5

Move the negative in front of the fraction.

$x = 1 - \frac{5}{7} - \frac{3 \cdot (- 1 (\frac{2}{7}))}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.6

Combine exponents.

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Step 5.2.1.1.1.6.1

Factor out negative.

$x = 1 - \frac{5}{7} - \frac{- (3 (\frac{2}{7}))}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.6.2

Combine $3$ and $\frac{2}{7}$ .

$x = 1 - \frac{5}{7} - \frac{- \frac{3 \cdot 2}{7}}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.1.6.3

Multiply $3$ by $2$ .

$x = 1 - \frac{5}{7} - \frac{- \frac{6}{7}}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} - \frac{- \frac{6}{7}}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} - \frac{- \frac{6}{7}}{2}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$x = 1 - \frac{5}{7} - (- \frac{6}{7} \cdot \frac{1}{2})$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.3

Cancel the common factor of $2$ .

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Step 5.2.1.1.3.1

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$x = 1 - \frac{5}{7} - (\frac{- 6}{7} \cdot \frac{1}{2})$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.3.2

Factor $2$ out of $- 6$ .

$x = 1 - \frac{5}{7} - (\frac{2 (- 3)}{7} \cdot \frac{1}{2})$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.3.3

Cancel the common factor.

$x = 1 - \frac{5}{7} - (\frac{2 \cdot - 3}{7} \cdot \frac{1}{2})$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.3.4

Rewrite the expression.

$x = 1 - \frac{5}{7} - \frac{- 3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} - \frac{- 3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.4

Move the negative in front of the fraction.

$x = 1 - \frac{5}{7} + \frac{3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.5

Multiply $- - \frac{3}{7}$ .

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Step 5.2.1.1.5.1

Multiply $- 1$ by $- 1$ .

$x = 1 - \frac{5}{7} + 1 (\frac{3}{7})$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.1.5.2

Multiply $\frac{3}{7}$ by $1$ .

$x = 1 - \frac{5}{7} + \frac{3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} + \frac{3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = 1 - \frac{5}{7} + \frac{3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.2

Combine fractions.

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Step 5.2.1.2.1

Combine the numerators over the common denominator.

$x = 1 + \frac{- 5 + 3}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.2.2

Simplify the expression.

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Step 5.2.1.2.2.1

Add $- 5$ and $3$ .

$x = 1 + \frac{- 2}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.2.2.2

Move the negative in front of the fraction.

$x = 1 - \frac{2}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.2.2.3

Write $1$ as a fraction with a common denominator.

$x = \frac{7}{7} - \frac{2}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.2.2.4

Combine the numerators over the common denominator.

$x = \frac{7 - 2}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

Step 5.2.1.2.2.5

Subtract $2$ from $7$ .

$x = \frac{5}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = \frac{5}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = \frac{5}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = \frac{5}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = \frac{5}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$

$x = \frac{5}{7}$

$y = - \frac{5}{7}$

$z = \frac{2 a}{7 (- a + 5)} - \frac{10}{7 (- a + 5)}$