Algebra Examples

$2 x + 4 y + 3 z = 6$ $5 x + 8 y + 6 z = 4$ $4 x + 5 y + 2 z = 6$

Step 1

Solve for $x$ in $2 x + 4 y + 3 z = 6$ .

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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.

$2 x + 3 z = 6 - 4 y$

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.1.2

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

$2 x = 6 - 4 y - 3 z$

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

$2 x = 6 - 4 y - 3 z$

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2

Divide each term in $2 x = 6 - 4 y - 3 z$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = 6 - 4 y - 3 z$ by $2$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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 $6$ by $2$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.3.1.2

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

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Step 1.2.3.1.2.1

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

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $2$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.3.1.2.2.2

Cancel the common factor.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.3.1.2.2.3

Rewrite the expression.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.3.1.2.2.4

Divide $- 2 y$ by $1$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 1.2.3.1.3

Move the negative in front of the fraction.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Step 2

Replace all occurrences of $x$ with $3 - 2 y - \frac{3 z}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $5 x + 8 y + 6 z = 4$ with $3 - 2 y - \frac{3 z}{2}$ .

$5 (3 - 2 y - \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (3 - 2 y - \frac{3 z}{2}) + 8 y + 6 z$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$5 \cdot 3 + 5 (- 2 y) + 5 (- \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $5$ by $3$ .

$15 + 5 (- 2 y) + 5 (- \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.1.2.2

Multiply $- 2$ by $5$ .

$15 - 10 y + 5 (- \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.1.2.3

Multiply $5 (- \frac{3 z}{2})$ .

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Step 2.2.1.1.2.3.1

Multiply $- 1$ by $5$ .

$15 - 10 y - 5 \frac{3 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.1.2.3.2

Combine $- 5$ and $\frac{3 z}{2}$ .

$15 - 10 y + \frac{- 5 (3 z)}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.1.2.3.3

Multiply $3$ by $- 5$ .

$15 - 10 y + \frac{- 15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 10 y + \frac{- 15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 10 y + \frac{- 15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.1.3

Move the negative in front of the fraction.

$15 - 10 y - \frac{15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 10 y - \frac{15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.2

Add $- 10 y$ and $8 y$ .

$15 - 2 y - \frac{15 z}{2} + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.3

To write $6 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$15 - 2 y - \frac{15 z}{2} + 6 z \cdot \frac{2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.4

Simplify terms.

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Step 2.2.1.4.1

Combine $6 z$ and $\frac{2}{2}$ .

$15 - 2 y - \frac{15 z}{2} + \frac{6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.4.2

Combine the numerators over the common denominator.

$15 - 2 y + \frac{- 15 z + 6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y + \frac{- 15 z + 6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5

Simplify each term.

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Step 2.2.1.5.1

Simplify the numerator.

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Step 2.2.1.5.1.1

Factor $3 z$ out of $- 15 z + 6 z \cdot 2$ .

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Step 2.2.1.5.1.1.1

Factor $3 z$ out of $- 15 z$ .

$15 - 2 y + \frac{3 z (- 5) + 6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5.1.1.2

Factor $3 z$ out of $6 z \cdot 2$ .

$15 - 2 y + \frac{3 z (- 5) + 3 z (2 \cdot 2)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5.1.1.3

Factor $3 z$ out of $3 z (- 5) + 3 z (2 \cdot 2)$ .

$15 - 2 y + \frac{3 z (- 5 + 2 \cdot 2)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y + \frac{3 z (- 5 + 2 \cdot 2)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5.1.2

Multiply $2$ by $2$ .

$15 - 2 y + \frac{3 z (- 5 + 4)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5.1.3

Add $- 5$ and $4$ .

$15 - 2 y + \frac{3 z \cdot - 1}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5.1.4

Multiply $- 1$ by $3$ .

$15 - 2 y + \frac{- 3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y + \frac{- 3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.2.1.5.2

Move the negative in front of the fraction.

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Step 2.3

Replace all occurrences of $x$ in $4 x + 5 y + 2 z = 6$ with $3 - 2 y - \frac{3 z}{2}$ .

$4 (3 - 2 y - \frac{3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4

Simplify the left side.

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Step 2.4.1

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

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$4 \cdot 3 + 4 (- 2 y) + 4 (- \frac{3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $4$ by $3$ .

$12 + 4 (- 2 y) + 4 (- \frac{3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2.2

Multiply $- 2$ by $4$ .

$12 - 8 y + 4 (- \frac{3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2.3

Cancel the common factor of $2$ .

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Step 2.4.1.1.2.3.1

Move the leading negative in $- \frac{3 z}{2}$ into the numerator.

$12 - 8 y + 4 (\frac{- 3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2.3.2

Factor $2$ out of $4$ .

$12 - 8 y + 2 (2) (\frac{- 3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2.3.3

Cancel the common factor.

$12 - 8 y + 2 \cdot (2 (\frac{- 3 z}{2})) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2.3.4

Rewrite the expression.

$12 - 8 y + 2 (- 3 z) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 8 y + 2 (- 3 z) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.1.2.4

Multiply $- 3$ by $2$ .

$12 - 8 y - 6 z + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 8 y - 6 z + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 8 y - 6 z + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $- 8 y$ and $5 y$ .

$12 - 3 y - 6 z + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 2.4.1.2.2

Add $- 6 z$ and $2 z$ .

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3

Solve for $y$ in $12 - 3 y - 4 z = 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $12$ from both sides of the equation.

$- 3 y - 4 z = 6 - 12$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.1.2

Add $4 z$ to both sides of the equation.

$- 3 y = 6 - 12 + 4 z$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.1.3

Subtract $12$ from $6$ .

$- 3 y = - 6 + 4 z$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$- 3 y = - 6 + 4 z$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.2

Divide each term in $- 3 y = - 6 + 4 z$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 y = - 6 + 4 z$ by $- 3$ .

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Divide $- 6$ by $- 3$ .

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 3.2.3.1.2

Move the negative in front of the fraction.

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Step 4

Replace all occurrences of $y$ with $2 - \frac{4 z}{3}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $15 - 2 y - \frac{3 z}{2} = 4$ with $2 - \frac{4 z}{3}$ .

$15 - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $15 - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2}$ .

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Step 4.2.1.1

Find the common denominator.

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Step 4.2.1.1.1

Write $15$ as a fraction with denominator $1$ .

$\frac{15}{1} - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Step 4.2.1.1.2

Multiply $\frac{15}{1}$ by $\frac{2}{2}$ .

$\frac{15}{1} \cdot \frac{2}{2} - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Step 4.2.1.1.3

Multiply $\frac{15}{1}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 2}{2} - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Step 4.2.1.1.4

Write $- 2 (2 - \frac{4 z}{3})$ as a fraction with denominator $1$ .

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3})}{1} - \frac{3 z}{2} = 4$

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

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

Step 4.2.1.1.5

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3})}{1} \cdot \frac{2}{2} - \frac{3 z}{2} = 4$

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

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

Step 4.2.1.1.6

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3}) \cdot 2}{2} - \frac{3 z}{2} = 4$

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

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

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3}) \cdot 2}{2} - \frac{3 z}{2} = 4$

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

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

Step 4.2.1.2

Combine the numerators over the common denominator.

$\frac{15 \cdot 2 - 2 (2 - \frac{4 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3

Simplify each term.

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Step 4.2.1.3.1

Multiply $15$ by $2$ .

$\frac{30 - 2 (2 - \frac{4 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.2

Apply the distributive property.

$\frac{30 + (- 2 \cdot 2 - 2 (- \frac{4 z}{3})) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.3

Multiply $- 2$ by $2$ .

$\frac{30 + (- 4 - 2 (- \frac{4 z}{3})) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.4

Multiply $- 2 (- \frac{4 z}{3})$ .

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Step 4.2.1.3.4.1

Multiply $- 1$ by $- 2$ .

$\frac{30 + (- 4 + 2 (\frac{4 z}{3})) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.4.2

Combine $2$ and $\frac{4 z}{3}$ .

$\frac{30 + (- 4 + \frac{2 (4 z)}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.4.3

Multiply $4$ by $2$ .

$\frac{30 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

$\frac{30 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.5

Apply the distributive property.

$\frac{30 - 4 \cdot 2 + \frac{8 z}{3} \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.6

Multiply $- 4$ by $2$ .

$\frac{30 - 8 + \frac{8 z}{3} \cdot 2 - 3 z}{2} = 4$

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

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

Step 4.2.1.3.7

Multiply $\frac{8 z}{3} \cdot 2$ .

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Step 4.2.1.3.7.1

Combine $\frac{8 z}{3}$ and $2$ .

$\frac{30 - 8 + \frac{8 z \cdot 2}{3} - 3 z}{2} = 4$

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

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

Step 4.2.1.3.7.2

Multiply $2$ by $8$ .

$\frac{30 - 8 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

$\frac{30 - 8 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

$\frac{30 - 8 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

Step 4.2.1.4

Subtract $8$ from $30$ .

$\frac{22 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

Step 4.2.1.5

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

$\frac{22 + \frac{16 z}{3} - 3 z \cdot \frac{3}{3}}{2} = 4$

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

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

Step 4.2.1.6

Simplify terms.

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Step 4.2.1.6.1

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

$\frac{22 + \frac{16 z}{3} + \frac{- 3 z \cdot 3}{3}}{2} = 4$

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

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

Step 4.2.1.6.2

Combine the numerators over the common denominator.

$\frac{22 + \frac{16 z - 3 z \cdot 3}{3}}{2} = 4$

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

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

Step 4.2.1.6.3

Simplify each term.

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Step 4.2.1.6.3.1

Simplify the numerator.

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Step 4.2.1.6.3.1.1

Factor $z$ out of $16 z - 3 z \cdot 3$ .

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Step 4.2.1.6.3.1.1.1

Factor $z$ out of $16 z$ .

$\frac{22 + \frac{z \cdot 16 - 3 z \cdot 3}{3}}{2} = 4$

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

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

Step 4.2.1.6.3.1.1.2

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

$\frac{22 + \frac{z \cdot 16 + z (- 3 \cdot 3)}{3}}{2} = 4$

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

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

Step 4.2.1.6.3.1.1.3

Factor $z$ out of $z \cdot 16 + z (- 3 \cdot 3)$ .

$\frac{22 + \frac{z (16 - 3 \cdot 3)}{3}}{2} = 4$

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

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

$\frac{22 + \frac{z (16 - 3 \cdot 3)}{3}}{2} = 4$

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

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

Step 4.2.1.6.3.1.2

Multiply $- 3$ by $3$ .

$\frac{22 + \frac{z (16 - 9)}{3}}{2} = 4$

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

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

Step 4.2.1.6.3.1.3

Subtract $9$ from $16$ .

$\frac{22 + \frac{z \cdot 7}{3}}{2} = 4$

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

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

$\frac{22 + \frac{z \cdot 7}{3}}{2} = 4$

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

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

Step 4.2.1.6.3.2

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

$\frac{22 + \frac{7 z}{3}}{2} = 4$

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

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

$\frac{22 + \frac{7 z}{3}}{2} = 4$

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

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

$\frac{22 + \frac{7 z}{3}}{2} = 4$

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

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

Step 4.2.1.7

Simplify the numerator.

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Step 4.2.1.7.1

To write $22$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{22 \cdot \frac{3}{3} + \frac{7 z}{3}}{2} = 4$

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

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

Step 4.2.1.7.2

Combine $22$ and $\frac{3}{3}$ .

$\frac{\frac{22 \cdot 3}{3} + \frac{7 z}{3}}{2} = 4$

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

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

Step 4.2.1.7.3

Combine the numerators over the common denominator.

$\frac{\frac{22 \cdot 3 + 7 z}{3}}{2} = 4$

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

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

Step 4.2.1.7.4

Multiply $22$ by $3$ .

$\frac{\frac{66 + 7 z}{3}}{2} = 4$

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

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

$\frac{\frac{66 + 7 z}{3}}{2} = 4$

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

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

Step 4.2.1.8

Multiply the numerator by the reciprocal of the denominator.

$\frac{66 + 7 z}{3} \cdot \frac{1}{2} = 4$

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

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

Step 4.2.1.9

Multiply $\frac{66 + 7 z}{3} \cdot \frac{1}{2}$ .

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Step 4.2.1.9.1

Multiply $\frac{66 + 7 z}{3}$ by $\frac{1}{2}$ .

$\frac{66 + 7 z}{3 \cdot 2} = 4$

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

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

Step 4.2.1.9.2

Multiply $3$ by $2$ .

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

Step 4.3

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

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $3 - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2}$ .

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Step 4.4.1.1

Find the common denominator.

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Step 4.4.1.1.1

Write $3$ as a fraction with denominator $1$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.1.2

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.1.3

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.1.4

Write $- 2 (2 - \frac{4 z}{3})$ as a fraction with denominator $1$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.1.5

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.1.6

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.2

Combine the numerators over the common denominator.

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

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3

Simplify each term.

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Step 4.4.1.3.1

Multiply $3$ by $2$ .

$x = \frac{6 - 2 (2 - \frac{4 z}{3}) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.2

Apply the distributive property.

$x = \frac{6 + (- 2 \cdot 2 - 2 (- \frac{4 z}{3})) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.3

Multiply $- 2$ by $2$ .

$x = \frac{6 + (- 4 - 2 (- \frac{4 z}{3})) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.4

Multiply $- 2 (- \frac{4 z}{3})$ .

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Step 4.4.1.3.4.1

Multiply $- 1$ by $- 2$ .

$x = \frac{6 + (- 4 + 2 (\frac{4 z}{3})) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.4.2

Combine $2$ and $\frac{4 z}{3}$ .

$x = \frac{6 + (- 4 + \frac{2 (4 z)}{3}) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.4.3

Multiply $4$ by $2$ .

$x = \frac{6 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{6 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.5

Apply the distributive property.

$x = \frac{6 - 4 \cdot 2 + \frac{8 z}{3} \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.6

Multiply $- 4$ by $2$ .

$x = \frac{6 - 8 + \frac{8 z}{3} \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.7

Multiply $\frac{8 z}{3} \cdot 2$ .

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Step 4.4.1.3.7.1

Combine $\frac{8 z}{3}$ and $2$ .

$x = \frac{6 - 8 + \frac{8 z \cdot 2}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.3.7.2

Multiply $2$ by $8$ .

$x = \frac{6 - 8 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{6 - 8 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{6 - 8 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.4

Subtract $8$ from $6$ .

$x = \frac{- 2 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.5

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

$x = \frac{- 2 + \frac{16 z}{3} - 3 z \cdot \frac{3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6

Simplify terms.

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Step 4.4.1.6.1

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

$x = \frac{- 2 + \frac{16 z}{3} + \frac{- 3 z \cdot 3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.2

Combine the numerators over the common denominator.

$x = \frac{- 2 + \frac{16 z - 3 z \cdot 3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.3

Simplify each term.

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Step 4.4.1.6.3.1

Simplify the numerator.

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Step 4.4.1.6.3.1.1

Factor $z$ out of $16 z - 3 z \cdot 3$ .

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Step 4.4.1.6.3.1.1.1

Factor $z$ out of $16 z$ .

$x = \frac{- 2 + \frac{z \cdot 16 - 3 z \cdot 3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.3.1.1.2

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

$x = \frac{- 2 + \frac{z \cdot 16 + z (- 3 \cdot 3)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.3.1.1.3

Factor $z$ out of $z \cdot 16 + z (- 3 \cdot 3)$ .

$x = \frac{- 2 + \frac{z (16 - 3 \cdot 3)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{z (16 - 3 \cdot 3)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.3.1.2

Multiply $- 3$ by $3$ .

$x = \frac{- 2 + \frac{z (16 - 9)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.3.1.3

Subtract $9$ from $16$ .

$x = \frac{- 2 + \frac{z \cdot 7}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{z \cdot 7}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.6.3.2

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

$x = \frac{- 2 + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.7

Simplify the numerator.

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Step 4.4.1.7.1

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

$x = \frac{- 2 \cdot \frac{3}{3} + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.7.2

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

$x = \frac{\frac{- 2 \cdot 3}{3} + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.7.3

Combine the numerators over the common denominator.

$x = \frac{\frac{- 2 \cdot 3 + 7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.7.4

Multiply $- 2$ by $3$ .

$x = \frac{\frac{- 6 + 7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{\frac{- 6 + 7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.8

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{- 6 + 7 z}{3} \cdot \frac{1}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.9

Multiply $\frac{- 6 + 7 z}{3} \cdot \frac{1}{2}$ .

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Step 4.4.1.9.1

Multiply $\frac{- 6 + 7 z}{3}$ by $\frac{1}{2}$ .

$x = \frac{- 6 + 7 z}{3 \cdot 2}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.9.2

Multiply $3$ by $2$ .

$x = \frac{- 6 + 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 6 + 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.10

Rewrite $- 6$ as $- 1 (6)$ .

$x = \frac{- 1 \cdot 6 + 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.11

Factor $- 1$ out of $7 z$ .

$x = \frac{- 1 \cdot 6 - (- 7 z)}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.12

Factor $- 1$ out of $- 1 (6) - (- 7 z)$ .

$x = \frac{- 1 (6 - 7 z)}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Step 4.4.1.13

Move the negative in front of the fraction.

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Step 5

Solve for $z$ in $\frac{66 + 7 z}{6} = 4$ .

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Step 5.1

Multiply both sides by $6$ .

$\frac{66 + 7 z}{6} \cdot 6 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.2

Simplify.

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Step 5.2.1

Simplify the left side.

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Step 5.2.1.1

Simplify $\frac{66 + 7 z}{6} \cdot 6$ .

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Step 5.2.1.1.1

Cancel the common factor of $6$ .

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Step 5.2.1.1.1.1

Cancel the common factor.

$\frac{66 + 7 z}{6} \cdot 6 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.2.1.1.1.2

Rewrite the expression.

$66 + 7 z = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

$66 + 7 z = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.2.1.1.2

Reorder $66$ and $7 z$ .

$7 z + 66 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Multiply $4$ by $6$ .

$7 z + 66 = 24$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 24$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 24$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.3

Solve for $z$ .

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Step 5.3.1

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

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Step 5.3.1.1

Subtract $66$ from both sides of the equation.

$7 z = 24 - 66$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.3.1.2

Subtract $66$ from $24$ .

$7 z = - 42$

$x = - \frac{6 - 7 z}{6}$

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

$7 z = - 42$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.3.2

Divide each term in $7 z = - 42$ by $7$ and simplify.

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Step 5.3.2.1

Divide each term in $7 z = - 42$ by $7$ .

$\frac{7 z}{7} = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.3.2.2

Simplify the left side.

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Step 5.3.2.2.1

Cancel the common factor of $7$ .

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Step 5.3.2.2.1.1

Cancel the common factor.

$\frac{7 z}{7} = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.3.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

$z = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

$z = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

Step 5.3.2.3

Simplify the right side.

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Step 5.3.2.3.1

Divide $- 42$ by $7$ .

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

Step 6

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

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Step 6.1

Replace all occurrences of $z$ in $x = - \frac{6 - 7 z}{6}$ with $- 6$ .

$x = - \frac{6 - 7 \cdot - 6}{6}$

$z = - 6$

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{6 - 7 \cdot - 6}{6}$ .

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Step 6.2.1.1

Cancel the common factor of $6 - 7 \cdot - 6$ and $6$ .

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Step 6.2.1.1.1

Rewrite $6$ as $- 1 (- 6)$ .

$x = - \frac{- 1 \cdot - 6 - 7 \cdot - 6}{6}$

$z = - 6$

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

Step 6.2.1.1.2

Factor $- 1$ out of $- 7 \cdot - 6$ .

$x = - \frac{- 1 \cdot - 6 - (7 \cdot - 6)}{6}$

$z = - 6$

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

Step 6.2.1.1.3

Factor $- 1$ out of $- 1 (- 6) - (7 \cdot - 6)$ .

$x = - \frac{- 1 (- 6 + 7 \cdot - 6)}{6}$

$z = - 6$

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

Step 6.2.1.1.4

Reorder terms.

$x = - \frac{- 1 (- 6 - 6 \cdot 7)}{6}$

$z = - 6$

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

Step 6.2.1.1.5

Factor $6$ out of $- 1 (- 6 - 6 \cdot 7)$ .

$x = - \frac{6 (- 1 (- 1 - 1 \cdot 7))}{6}$

$z = - 6$

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

Step 6.2.1.1.6

Cancel the common factors.

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Step 6.2.1.1.6.1

Factor $6$ out of $6$ .

$x = - \frac{6 (- 1 (- 1 - 1 \cdot 7))}{6 (1)}$

$z = - 6$

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

Step 6.2.1.1.6.2

Cancel the common factor.

$x = - \frac{6 (- 1 (- 1 - 1 \cdot 7))}{6 \cdot 1}$

$z = - 6$

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

Step 6.2.1.1.6.3

Rewrite the expression.

$x = - \frac{- 1 (- 1 - 1 \cdot 7)}{1}$

$z = - 6$

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

Step 6.2.1.1.6.4

Divide $- 1 (- 1 - 1 \cdot 7)$ by $1$ .

$x = - (- 1 (- 1 - 1 \cdot 7))$

$z = - 6$

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

$x = - (- 1 (- 1 - 1 \cdot 7))$

$z = - 6$

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

$x = - (- 1 (- 1 - 1 \cdot 7))$

$z = - 6$

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

Step 6.2.1.2

Simplify the expression.

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Step 6.2.1.2.1

Rewrite $- 1 (- 1 - 1 \cdot 7)$ as $- (- 1 - 1 \cdot 7)$ .

$x = - 1 - 1 \cdot 7$

$z = - 6$

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

Step 6.2.1.2.2

Multiply $- 1$ by $7$ .

$x = - 1 - 7$

$z = - 6$

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

Step 6.2.1.2.3

Subtract $7$ from $- 1$ .

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

Step 6.2.1.3

Multiply $- - - 8$ .

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Step 6.2.1.3.1

Multiply $- 1$ by $- 8$ .

$x = - 1 \cdot 8$

$z = - 6$

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

Step 6.2.1.3.2

Multiply $- 1$ by $8$ .

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

Step 6.3

Replace all occurrences of $z$ in $y = 2 - \frac{4 z}{3}$ with $- 6$ .

$y = 2 - \frac{4 (- 6)}{3}$

$x = - 8$

$z = - 6$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $2 - \frac{4 (- 6)}{3}$ .

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Step 6.4.1.1

Simplify each term.

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Step 6.4.1.1.1

Cancel the common factor of $- 6$ and $3$ .

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Step 6.4.1.1.1.1

Factor $3$ out of $4 (- 6)$ .

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

$x = - 8$

$z = - 6$

Step 6.4.1.1.1.2

Cancel the common factors.

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Step 6.4.1.1.1.2.1

Factor $3$ out of $3$ .

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

$x = - 8$

$z = - 6$

Step 6.4.1.1.1.2.2

Cancel the common factor.

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

$x = - 8$

$z = - 6$

Step 6.4.1.1.1.2.3

Rewrite the expression.

$y = 2 - \frac{4 \cdot (- 2)}{1}$

$x = - 8$

$z = - 6$

Step 6.4.1.1.1.2.4

Divide $4 \cdot (- 2)$ by $1$ .

$y = 2 - (4 \cdot (- 2))$

$x = - 8$

$z = - 6$

$y = 2 - (4 \cdot (- 2))$

$x = - 8$

$z = - 6$

$y = 2 - (4 \cdot (- 2))$

$x = - 8$

$z = - 6$

Step 6.4.1.1.2

Multiply $- (4 \cdot (- 2))$ .

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Step 6.4.1.1.2.1

Multiply $4$ by $- 2$ .

$y = 2 + 8$

$x = - 8$

$z = - 6$

Step 6.4.1.1.2.2

Multiply $- 1$ by $- 8$ .

$y = 2 + 8$

$x = - 8$

$z = - 6$

$y = 2 + 8$

$x = - 8$

$z = - 6$

$y = 2 + 8$

$x = - 8$

$z = - 6$

Step 6.4.1.2

Add $2$ and $8$ .

$y = 10$

$x = - 8$

$z = - 6$

$y = 10$

$x = - 8$

$z = - 6$

$y = 10$

$x = - 8$

$z = - 6$

$y = 10$

$x = - 8$

$z = - 6$

Step 7

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

$(- 8, 10, - 6)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 8, 10, - 6)$

Equation Form:

$x = - 8, y = 10, z = - 6$