Algebra Examples

$10 x + 4 y - 2 z = - 15$ $- 8 y + 9 z = 70$ $3 y - 2 z = - 18$

Step 1

Solve for $x$ in $10 x + 4 y - 2 z = - 15$ .

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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

Subtract $4 y$ from both sides of the equation.

$10 x - 2 z = - 15 - 4 y$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.1.2

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

$10 x = - 15 - 4 y + 2 z$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$10 x = - 15 - 4 y + 2 z$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2

Divide each term in $10 x = - 15 - 4 y + 2 z$ by $10$ and simplify.

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Step 1.2.1

Divide each term in $10 x = - 15 - 4 y + 2 z$ by $10$ .

$\frac{10 x}{10} = \frac{- 15}{10} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $10$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{- 15}{10} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 15}{10} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = \frac{- 15}{10} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = \frac{- 15}{10} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

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

Cancel the common factor of $- 15$ and $10$ .

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Step 1.2.3.1.1.1

Factor $5$ out of $- 15$ .

$x = \frac{5 (- 3)}{10} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $5$ out of $10$ .

$x = \frac{5 \cdot - 3}{5 \cdot 2} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{5 \cdot - 3}{5 \cdot 2} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{- 3}{2} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = \frac{- 3}{2} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = \frac{- 3}{2} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = - \frac{3}{2} + \frac{- 4 y}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.3

Cancel the common factor of $- 4$ and $10$ .

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Step 1.2.3.1.3.1

Factor $2$ out of $- 4 y$ .

$x = - \frac{3}{2} + \frac{2 (- 2 y)}{10} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.3.2

Cancel the common factors.

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Step 1.2.3.1.3.2.1

Factor $2$ out of $10$ .

$x = - \frac{3}{2} + \frac{2 (- 2 y)}{2 (5)} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.3.2.2

Cancel the common factor.

$x = - \frac{3}{2} + \frac{2 (- 2 y)}{2 \cdot 5} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.3.2.3

Rewrite the expression.

$x = - \frac{3}{2} + \frac{- 2 y}{5} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{- 2 y}{5} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{- 2 y}{5} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.4

Move the negative in front of the fraction.

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{2 z}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.5

Cancel the common factor of $2$ and $10$ .

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Step 1.2.3.1.5.1

Factor $2$ out of $2 z$ .

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{2 (z)}{10}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.5.2

Cancel the common factors.

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Step 1.2.3.1.5.2.1

Factor $2$ out of $10$ .

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{2 z}{2 \cdot 5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.5.2.2

Cancel the common factor.

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{2 z}{2 \cdot 5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 1.2.3.1.5.2.3

Rewrite the expression.

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$- 8 y + 9 z = 70$

$3 y - 2 z = - 18$

Step 2

Solve for $y$ in $- 8 y + 9 z = 70$ .

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Step 2.1

Subtract $9 z$ from both sides of the equation.

$- 8 y = 70 - 9 z$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2

Divide each term in $- 8 y = 70 - 9 z$ by $- 8$ and simplify.

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Step 2.2.1

Divide each term in $- 8 y = 70 - 9 z$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{70}{- 8} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 8$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{70}{- 8} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{70}{- 8} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = \frac{70}{- 8} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = \frac{70}{- 8} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Cancel the common factor of $70$ and $- 8$ .

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Step 2.2.3.1.1.1

Factor $2$ out of $70$ .

$y = \frac{2 (35)}{- 8} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.3.1.1.2

Cancel the common factors.

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Step 2.2.3.1.1.2.1

Factor $2$ out of $- 8$ .

$y = \frac{2 \cdot 35}{2 \cdot - 4} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 35}{2 \cdot - 4} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{35}{- 4} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = \frac{35}{- 4} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = \frac{35}{- 4} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{35}{4} + \frac{- 9 z}{- 8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 2.2.3.1.3

Dividing two negative values results in a positive value.

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$

$3 y - 2 z = - 18$

Step 3

Replace all occurrences of $y$ with $- \frac{35}{4} + \frac{9 z}{8}$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $x = - \frac{3}{2} - \frac{2 y}{5} + \frac{z}{5}$ with $- \frac{35}{4} + \frac{9 z}{8}$ .

$x = - \frac{3}{2} - \frac{2 (- \frac{35}{4} + \frac{9 z}{8})}{5} + \frac{z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{3}{2} - \frac{2 (- \frac{35}{4} + \frac{9 z}{8})}{5} + \frac{z}{5}$ .

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Step 3.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 3}{2} + \frac{- 2 (- \frac{35}{4} + \frac{9 z}{8}) + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2

Simplify each term.

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Step 3.2.1.2.1

Apply the distributive property.

$x = \frac{- 3}{2} + \frac{- 2 (- \frac{35}{4}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.2

Cancel the common factor of $2$ .

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Step 3.2.1.2.2.1

Move the leading negative in $- \frac{35}{4}$ into the numerator.

$x = \frac{- 3}{2} + \frac{- 2 (\frac{- 35}{4}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.2.2

Factor $2$ out of $- 2$ .

$x = \frac{- 3}{2} + \frac{2 (- 1) (\frac{- 35}{4}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.2.3

Factor $2$ out of $4$ .

$x = \frac{- 3}{2} + \frac{2 \cdot (- 1 \frac{- 35}{2 \cdot 2}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.2.4

Cancel the common factor.

$x = \frac{- 3}{2} + \frac{2 \cdot (- 1 \frac{- 35}{2 \cdot 2}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.2.5

Rewrite the expression.

$x = \frac{- 3}{2} + \frac{- 1 (\frac{- 35}{2}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = \frac{- 3}{2} + \frac{- 1 (\frac{- 35}{2}) - 2 \frac{9 z}{8} + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.3

Cancel the common factor of $2$ .

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Step 3.2.1.2.3.1

Factor $2$ out of $- 2$ .

$x = \frac{- 3}{2} + \frac{- 1 (\frac{- 35}{2}) + 2 (- 1) (\frac{9 z}{8}) + z}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.3.2

Factor $2$ out of $8$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.3.3

Cancel the common factor.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.3.4

Rewrite the expression.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.4

Simplify each term.

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Step 3.2.1.2.4.1

Move the negative in front of the fraction.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.4.2

Multiply $- 1 (- \frac{35}{2})$ .

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Step 3.2.1.2.4.2.1

Multiply $- 1$ by $- 1$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.4.2.2

Multiply $\frac{35}{2}$ by $1$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.2.4.3

Rewrite $- 1 \frac{9 z}{4}$ as $- \frac{9 z}{4}$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.3

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

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.4

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

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.5

Combine the numerators over the common denominator.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.6

Add $- 9 z$ and $z \cdot 4$ .

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Step 3.2.1.6.1

Reorder $z$ and $4$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.6.2

Add $- 9 z$ and $4 \cdot z$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.7

Move the negative in front of the fraction.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8

Simplify each term.

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Step 3.2.1.8.1

Move the negative in front of the fraction.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2

Simplify the numerator.

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Step 3.2.1.8.2.1

To write $\frac{35}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.2

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

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Step 3.2.1.8.2.2.1

Multiply $\frac{35}{2}$ by $\frac{2}{2}$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.2.2

Multiply $2$ by $2$ .

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.3

Combine the numerators over the common denominator.

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

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.4

Simplify the numerator.

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Step 3.2.1.8.2.4.1

Factor $5$ out of $35 \cdot 2 - 5 z$ .

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Step 3.2.1.8.2.4.1.1

Factor $5$ out of $35 \cdot 2$ .

$x = - \frac{3}{2} + \frac{\frac{5 (7 \cdot 2) - 5 z}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.4.1.2

Factor $5$ out of $- 5 z$ .

$x = - \frac{3}{2} + \frac{\frac{5 (7 \cdot 2) + 5 (- z)}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.4.1.3

Factor $5$ out of $5 (7 \cdot 2) + 5 (- z)$ .

$x = - \frac{3}{2} + \frac{\frac{5 (7 \cdot 2 - z)}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{\frac{5 (7 \cdot 2 - z)}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.2.4.2

Multiply $7$ by $2$ .

$x = - \frac{3}{2} + \frac{\frac{5 (14 - z)}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{\frac{5 (14 - z)}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{\frac{5 (14 - z)}{4}}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.3

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3}{2} + \frac{5 (14 - z)}{4} \cdot \frac{1}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.4

Cancel the common factor of $5$ .

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Step 3.2.1.8.4.1

Cancel the common factor.

$x = - \frac{3}{2} + \frac{5 (14 - z)}{4} \cdot \frac{1}{5}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.8.4.2

Rewrite the expression.

$x = - \frac{3}{2} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = - \frac{3}{2} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.9

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

$x = - \frac{3}{2} \cdot \frac{2}{2} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.10

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

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Step 3.2.1.10.1

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

$x = - \frac{3 \cdot 2}{2 \cdot 2} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.10.2

Multiply $2$ by $2$ .

$x = - \frac{3 \cdot 2}{4} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = - \frac{3 \cdot 2}{4} + \frac{14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.11

Combine the numerators over the common denominator.

$x = \frac{- 3 \cdot 2 + 14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.12

Simplify the numerator.

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Step 3.2.1.12.1

Multiply $- 3$ by $2$ .

$x = \frac{- 6 + 14 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.2.1.12.2

Add $- 6$ and $14$ .

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$3 y - 2 z = - 18$

Step 3.3

Replace all occurrences of $y$ in $3 y - 2 z = - 18$ with $- \frac{35}{4} + \frac{9 z}{8}$ .

$3 (- \frac{35}{4} + \frac{9 z}{8}) - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4

Simplify the left side.

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Step 3.4.1

Simplify $3 (- \frac{35}{4} + \frac{9 z}{8}) - 2 z$ .

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Step 3.4.1.1

Simplify each term.

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Step 3.4.1.1.1

Apply the distributive property.

$3 (- \frac{35}{4}) + 3 (\frac{9 z}{8}) - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.1.2

Multiply $3 (- \frac{35}{4})$ .

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Step 3.4.1.1.2.1

Multiply $- 1$ by $3$ .

$- 3 (\frac{35}{4}) + 3 (\frac{9 z}{8}) - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.1.2.2

Combine $- 3$ and $\frac{35}{4}$ .

$\frac{- 3 \cdot 35}{4} + 3 (\frac{9 z}{8}) - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.1.2.3

Multiply $- 3$ by $35$ .

$\frac{- 105}{4} + 3 (\frac{9 z}{8}) - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$\frac{- 105}{4} + 3 (\frac{9 z}{8}) - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.1.3

Multiply $3 \frac{9 z}{8}$ .

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Step 3.4.1.1.3.1

Combine $3$ and $\frac{9 z}{8}$ .

$\frac{- 105}{4} + \frac{3 (9 z)}{8} - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.1.3.2

Multiply $9$ by $3$ .

$\frac{- 105}{4} + \frac{27 z}{8} - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$\frac{- 105}{4} + \frac{27 z}{8} - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.1.4

Move the negative in front of the fraction.

$- \frac{105}{4} + \frac{27 z}{8} - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{27 z}{8} - 2 z = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.2

To write $- 2 z$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{105}{4} + \frac{27 z}{8} - 2 z \cdot \frac{8}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.3

Simplify terms.

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Step 3.4.1.3.1

Combine $- 2 z$ and $\frac{8}{8}$ .

$- \frac{105}{4} + \frac{27 z}{8} + \frac{- 2 z \cdot 8}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.3.2

Combine the numerators over the common denominator.

$- \frac{105}{4} + \frac{27 z - 2 z \cdot 8}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{27 z - 2 z \cdot 8}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.4

Simplify each term.

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Step 3.4.1.4.1

Simplify the numerator.

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Step 3.4.1.4.1.1

Factor $z$ out of $27 z - 2 z \cdot 8$ .

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Step 3.4.1.4.1.1.1

Factor $z$ out of $27 z$ .

$- \frac{105}{4} + \frac{z \cdot 27 - 2 z \cdot 8}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.4.1.1.2

Factor $z$ out of $- 2 z \cdot 8$ .

$- \frac{105}{4} + \frac{z \cdot 27 + z (- 2 \cdot 8)}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.4.1.1.3

Factor $z$ out of $z \cdot 27 + z (- 2 \cdot 8)$ .

$- \frac{105}{4} + \frac{z (27 - 2 \cdot 8)}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{z (27 - 2 \cdot 8)}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.4.1.2

Multiply $- 2$ by $8$ .

$- \frac{105}{4} + \frac{z (27 - 16)}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.4.1.3

Subtract $16$ from $27$ .

$- \frac{105}{4} + \frac{z \cdot 11}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{z \cdot 11}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 3.4.1.4.2

Move $11$ to the left of $z$ .

$- \frac{105}{4} + \frac{11 z}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{11 z}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{11 z}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{11 z}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$- \frac{105}{4} + \frac{11 z}{8} = - 18$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4

Solve for $z$ in $- \frac{105}{4} + \frac{11 z}{8} = - 18$ .

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Step 4.1

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

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Step 4.1.1

Add $\frac{105}{4}$ to both sides of the equation.

$\frac{11 z}{8} = - 18 + \frac{105}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.1.2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{11 z}{8} = - 18 \cdot \frac{4}{4} + \frac{105}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.1.3

Combine $- 18$ and $\frac{4}{4}$ .

$\frac{11 z}{8} = \frac{- 18 \cdot 4}{4} + \frac{105}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.1.4

Combine the numerators over the common denominator.

$\frac{11 z}{8} = \frac{- 18 \cdot 4 + 105}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.1.5

Simplify the numerator.

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Step 4.1.5.1

Multiply $- 18$ by $4$ .

$\frac{11 z}{8} = \frac{- 72 + 105}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.1.5.2

Add $- 72$ and $105$ .

$\frac{11 z}{8} = \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$\frac{11 z}{8} = \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$\frac{11 z}{8} = \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.2

Multiply both sides of the equation by $\frac{8}{11}$ .

$\frac{8}{11} \cdot \frac{11 z}{8} = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Simplify $\frac{8}{11} \cdot \frac{11 z}{8}$ .

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Step 4.3.1.1.1

Cancel the common factor of $8$ .

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Step 4.3.1.1.1.1

Cancel the common factor.

$\frac{8}{11} \cdot \frac{11 z}{8} = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.1.1.1.2

Rewrite the expression.

$\frac{1}{11} \cdot (11 z) = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$\frac{1}{11} \cdot (11 z) = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.1.1.2

Cancel the common factor of $11$ .

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Step 4.3.1.1.2.1

Factor $11$ out of $11 z$ .

$\frac{1}{11} \cdot (11 (z)) = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.1.1.2.2

Cancel the common factor.

$\frac{1}{11} \cdot (11 z) = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.1.1.2.3

Rewrite the expression.

$z = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = \frac{8}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Simplify $\frac{8}{11} \cdot \frac{33}{4}$ .

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Step 4.3.2.1.1

Cancel the common factor of $4$ .

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Step 4.3.2.1.1.1

Factor $4$ out of $8$ .

$z = \frac{4 (2)}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2.1.1.2

Cancel the common factor.

$z = \frac{4 \cdot 2}{11} \cdot \frac{33}{4}$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2.1.1.3

Rewrite the expression.

$z = \frac{2}{11} \cdot 33$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = \frac{2}{11} \cdot 33$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2.1.2

Cancel the common factor of $11$ .

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Step 4.3.2.1.2.1

Factor $11$ out of $33$ .

$z = \frac{2}{11} \cdot (11 (3))$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2.1.2.2

Cancel the common factor.

$z = \frac{2}{11} \cdot (11 \cdot 3)$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2.1.2.3

Rewrite the expression.

$z = 2 \cdot 3$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = 2 \cdot 3$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 4.3.2.1.3

Multiply $2$ by $3$ .

$z = 6$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = 6$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = 6$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = 6$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$z = 6$

$x = \frac{8 - z}{4}$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5

Replace all occurrences of $z$ with $6$ in each equation.

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Step 5.1

Replace all occurrences of $z$ in $x = \frac{8 - z}{4}$ with $6$ .

$x = \frac{8 - (6)}{4}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{8 - (6)}{4}$ .

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Step 5.2.1.1

Cancel the common factor of $8 - (6)$ and $4$ .

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Step 5.2.1.1.1

Rewrite $8$ as $- 1 (- 8)$ .

$x = \frac{- 1 \cdot - 8 - (6)}{4}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.1.2

Factor $- 1$ out of $- 1 (- 8) - (6)$ .

$x = \frac{- 1 (- 8 + 6)}{4}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.1.3

Factor $2$ out of $- 1 (- 8 + 6)$ .

$x = \frac{2 (- 1 (- 4 + 3))}{4}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.1.4

Cancel the common factors.

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Step 5.2.1.1.4.1

Factor $2$ out of $4$ .

$x = \frac{2 (- 1 (- 4 + 3))}{2 (2)}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.1.4.2

Cancel the common factor.

$x = \frac{2 (- 1 (- 4 + 3))}{2 \cdot 2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.1.4.3

Rewrite the expression.

$x = \frac{- 1 (- 4 + 3)}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = \frac{- 1 (- 4 + 3)}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = \frac{- 1 (- 4 + 3)}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.2

Simplify the expression.

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Step 5.2.1.2.1

Add $- 4$ and $3$ .

$x = \frac{- 1 \cdot - 1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.2.1.2.2

Multiply $- 1$ by $- 1$ .

$x = \frac{1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = \frac{1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = \frac{1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

$x = \frac{1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{9 z}{8}$

Step 5.3

Replace all occurrences of $z$ in $y = - \frac{35}{4} + \frac{9 z}{8}$ with $6$ .

$y = - \frac{35}{4} + \frac{9 (6)}{8}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4

Simplify the right side.

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Step 5.4.1

Simplify $- \frac{35}{4} + \frac{9 (6)}{8}$ .

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Step 5.4.1.1

Multiply $9$ by $6$ .

$y = - \frac{35}{4} + \frac{54}{8}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.2

Cancel the common factor of $54$ and $8$ .

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Step 5.4.1.2.1

Factor $2$ out of $54$ .

$y = - \frac{35}{4} + \frac{2 (27)}{8}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.2.2

Cancel the common factors.

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Step 5.4.1.2.2.1

Factor $2$ out of $8$ .

$y = - \frac{35}{4} + \frac{2 \cdot 27}{2 \cdot 4}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.2.2.2

Cancel the common factor.

$y = - \frac{35}{4} + \frac{2 \cdot 27}{2 \cdot 4}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.2.2.3

Rewrite the expression.

$y = - \frac{35}{4} + \frac{27}{4}$

$x = \frac{1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{27}{4}$

$x = \frac{1}{2}$

$z = 6$

$y = - \frac{35}{4} + \frac{27}{4}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.3

Combine the numerators over the common denominator.

$y = \frac{- 35 + 27}{4}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.4

Simplify the expression.

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Step 5.4.1.4.1

Add $- 35$ and $27$ .

$y = \frac{- 8}{4}$

$x = \frac{1}{2}$

$z = 6$

Step 5.4.1.4.2

Divide $- 8$ by $4$ .

$y = - 2$

$x = \frac{1}{2}$

$z = 6$

$y = - 2$

$x = \frac{1}{2}$

$z = 6$

$y = - 2$

$x = \frac{1}{2}$

$z = 6$

$y = - 2$

$x = \frac{1}{2}$

$z = 6$

$y = - 2$

$x = \frac{1}{2}$

$z = 6$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{1}{2}, - 2, 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{2}, - 2, 6)$

Equation Form:

$x = \frac{1}{2}, y = - 2, z = 6$