Precalculus Examples

$3 x - 5 y + z = 9$ , $x - 3 y - 2 z = - 8$ , $5 x - 6 y + 3 z = 15$

Step 1

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

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Step 1.1

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

$- 5 y + z = 9 - 3 x$

$x - 3 y - 2 z = - 8$

$5 x - 6 y + 3 z = 15$

Step 1.2

Add $5 y$ to both sides of the equation.

$z = 9 - 3 x + 5 y$

$x - 3 y - 2 z = - 8$

$5 x - 6 y + 3 z = 15$

$z = 9 - 3 x + 5 y$

$x - 3 y - 2 z = - 8$

$5 x - 6 y + 3 z = 15$

Step 2

Replace all occurrences of $z$ with $9 - 3 x + 5 y$ in each equation.

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Step 2.1

Replace all occurrences of $z$ in $x - 3 y - 2 z = - 8$ with $9 - 3 x + 5 y$ .

$x - 3 y - 2 (9 - 3 x + 5 y) = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x - 3 y - 2 (9 - 3 x + 5 y)$ .

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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.

$x - 3 y - 2 \cdot 9 - 2 (- 3 x) - 2 (5 y) = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $- 2$ by $9$ .

$x - 3 y - 18 - 2 (- 3 x) - 2 (5 y) = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.2.1.1.2.2

Multiply $- 3$ by $- 2$ .

$x - 3 y - 18 + 6 x - 2 (5 y) = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.2.1.1.2.3

Multiply $5$ by $- 2$ .

$x - 3 y - 18 + 6 x - 10 y = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

$x - 3 y - 18 + 6 x - 10 y = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

$x - 3 y - 18 + 6 x - 10 y = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $x$ and $6 x$ .

$7 x - 3 y - 18 - 10 y = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.2.1.2.2

Subtract $10 y$ from $- 3 y$ .

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 3 z = 15$

Step 2.3

Replace all occurrences of $z$ in $5 x - 6 y + 3 z = 15$ with $9 - 3 x + 5 y$ .

$5 x - 6 y + 3 (9 - 3 x + 5 y) = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $5 x - 6 y + 3 (9 - 3 x + 5 y)$ .

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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.

$5 x - 6 y + 3 \cdot 9 + 3 (- 3 x) + 3 (5 y) = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $3$ by $9$ .

$5 x - 6 y + 27 + 3 (- 3 x) + 3 (5 y) = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 2.4.1.1.2.2

Multiply $- 3$ by $3$ .

$5 x - 6 y + 27 - 9 x + 3 (5 y) = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 2.4.1.1.2.3

Multiply $5$ by $3$ .

$5 x - 6 y + 27 - 9 x + 15 y = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 27 - 9 x + 15 y = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$5 x - 6 y + 27 - 9 x + 15 y = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Subtract $9 x$ from $5 x$ .

$- 4 x - 6 y + 27 + 15 y = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 2.4.1.2.2

Add $- 6 y$ and $15 y$ .

$- 4 x + 9 y + 27 = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$- 4 x + 9 y + 27 = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$- 4 x + 9 y + 27 = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$- 4 x + 9 y + 27 = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$- 4 x + 9 y + 27 = 15$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3

Solve for $x$ in $- 4 x + 9 y + 27 = 15$ .

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Step 3.1

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

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Step 3.1.1

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

$- 4 x + 27 = 15 - 9 y$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3.1.2

Subtract $27$ from both sides of the equation.

$- 4 x = 15 - 9 y - 27$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3.1.3

Subtract $27$ from $15$ .

$- 4 x = - 9 y - 12$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$- 4 x = - 9 y - 12$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3.2

Divide each term in $- 4 x = - 9 y - 12$ by $- 4$ and simplify.

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Step 3.2.1

Divide each term in $- 4 x = - 9 y - 12$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 9 y}{- 4} + \frac{- 12}{- 4}$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 9 y}{- 4} + \frac{- 12}{- 4}$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9 y}{- 4} + \frac{- 12}{- 4}$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$x = \frac{- 9 y}{- 4} + \frac{- 12}{- 4}$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$x = \frac{- 9 y}{- 4} + \frac{- 12}{- 4}$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

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

Dividing two negative values results in a positive value.

$x = \frac{9 y}{4} + \frac{- 12}{- 4}$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 3.2.3.1.2

Divide $- 12$ by $- 4$ .

$x = \frac{9 y}{4} + 3$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$x = \frac{9 y}{4} + 3$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$x = \frac{9 y}{4} + 3$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$x = \frac{9 y}{4} + 3$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

$x = \frac{9 y}{4} + 3$

$7 x - 13 y - 18 = - 8$

$z = 9 - 3 x + 5 y$

Step 4

Replace all occurrences of $x$ with $\frac{9 y}{4} + 3$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $7 x - 13 y - 18 = - 8$ with $\frac{9 y}{4} + 3$ .

$7 (\frac{9 y}{4} + 3) - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $7 (\frac{9 y}{4} + 3) - 13 y - 18$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Apply the distributive property.

$7 (\frac{9 y}{4}) + 7 \cdot 3 - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.1.2

Multiply $7 \frac{9 y}{4}$ .

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Step 4.2.1.1.2.1

Combine $7$ and $\frac{9 y}{4}$ .

$\frac{7 (9 y)}{4} + 7 \cdot 3 - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.1.2.2

Multiply $9$ by $7$ .

$\frac{63 y}{4} + 7 \cdot 3 - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{63 y}{4} + 7 \cdot 3 - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.1.3

Multiply $7$ by $3$ .

$\frac{63 y}{4} + 21 - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{63 y}{4} + 21 - 13 y - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.2

To write $- 13 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{63 y}{4} - 13 y \cdot \frac{4}{4} + 21 - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.3

Combine $- 13 y$ and $\frac{4}{4}$ .

$\frac{63 y}{4} + \frac{- 13 y \cdot 4}{4} + 21 - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{63 y - 13 y \cdot 4}{4} + 21 - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.5

Find the common denominator.

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Step 4.2.1.5.1

Write $21$ as a fraction with denominator $1$ .

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21}{1} - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.5.2

Multiply $\frac{21}{1}$ by $\frac{4}{4}$ .

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21}{1} \cdot \frac{4}{4} - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.5.3

Multiply $\frac{21}{1}$ by $\frac{4}{4}$ .

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21 \cdot 4}{4} - 18 = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.5.4

Write $- 18$ as a fraction with denominator $1$ .

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 18}{1} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.5.5

Multiply $\frac{- 18}{1}$ by $\frac{4}{4}$ .

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 18}{1} \cdot \frac{4}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.5.6

Multiply $\frac{- 18}{1}$ by $\frac{4}{4}$ .

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 18 \cdot 4}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{63 y - 13 y \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 18 \cdot 4}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.6

Combine the numerators over the common denominator.

$\frac{63 y - 13 y \cdot 4 + 21 \cdot 4 - 18 \cdot 4}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.7

Simplify each term.

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Step 4.2.1.7.1

Multiply $4$ by $- 13$ .

$\frac{63 y - 52 y + 21 \cdot 4 - 18 \cdot 4}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.7.2

Multiply $21$ by $4$ .

$\frac{63 y - 52 y + 84 - 18 \cdot 4}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.7.3

Multiply $- 18$ by $4$ .

$\frac{63 y - 52 y + 84 - 72}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{63 y - 52 y + 84 - 72}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.8

Simplify by adding terms.

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Step 4.2.1.8.1

Subtract $52 y$ from $63 y$ .

$\frac{11 y + 84 - 72}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.2.1.8.2

Subtract $72$ from $84$ .

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - 3 x + 5 y$

Step 4.3

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

$z = 9 - 3 (\frac{9 y}{4} + 3) + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $9 - 3 (\frac{9 y}{4} + 3) + 5 y$ .

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Step 4.4.1.1

Simplify each term.

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Step 4.4.1.1.1

Apply the distributive property.

$z = 9 - 3 \frac{9 y}{4} - 3 \cdot 3 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.1.2

Multiply $- 3 \frac{9 y}{4}$ .

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Step 4.4.1.1.2.1

Combine $- 3$ and $\frac{9 y}{4}$ .

$z = 9 + \frac{- 3 (9 y)}{4} - 3 \cdot 3 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.1.2.2

Multiply $9$ by $- 3$ .

$z = 9 + \frac{- 27 y}{4} - 3 \cdot 3 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 + \frac{- 27 y}{4} - 3 \cdot 3 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.1.3

Multiply $- 3$ by $3$ .

$z = 9 + \frac{- 27 y}{4} - 9 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$z = 9 - \frac{27 y}{4} - 9 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = 9 - \frac{27 y}{4} - 9 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.2

Combine the opposite terms in $9 - \frac{27 y}{4} - 9 + 5 y$ .

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Step 4.4.1.2.1

Subtract $9$ from $9$ .

$z = - \frac{27 y}{4} + 0 + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.2.2

Add $- \frac{27 y}{4}$ and $0$ .

$z = - \frac{27 y}{4} + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = - \frac{27 y}{4} + 5 y$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.3

To write $5 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$z = - \frac{27 y}{4} + 5 y \cdot \frac{4}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.4

Simplify terms.

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Step 4.4.1.4.1

Combine $5 y$ and $\frac{4}{4}$ .

$z = - \frac{27 y}{4} + \frac{5 y \cdot 4}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.4.2

Combine the numerators over the common denominator.

$z = \frac{- 27 y + 5 y \cdot 4}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = \frac{- 27 y + 5 y \cdot 4}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Factor $y$ out of $- 27 y + 5 y \cdot 4$ .

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Step 4.4.1.5.1.1

Factor $y$ out of $- 27 y$ .

$z = \frac{y \cdot - 27 + 5 y \cdot 4}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.5.1.2

Factor $y$ out of $5 y \cdot 4$ .

$z = \frac{y \cdot - 27 + y (5 \cdot 4)}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.5.1.3

Factor $y$ out of $y \cdot - 27 + y (5 \cdot 4)$ .

$z = \frac{y (- 27 + 5 \cdot 4)}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = \frac{y (- 27 + 5 \cdot 4)}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.5.2

Multiply $5$ by $4$ .

$z = \frac{y (- 27 + 20)}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.5.3

Add $- 27$ and $20$ .

$z = \frac{y \cdot - 7}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = \frac{y \cdot - 7}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.6

Simplify the expression.

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Step 4.4.1.6.1

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

$z = \frac{- 7 \cdot y}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 4.4.1.6.2

Move the negative in front of the fraction.

$z = - \frac{7 y}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = - \frac{7 y}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = - \frac{7 y}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = - \frac{7 y}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

$z = - \frac{7 y}{4}$

$\frac{11 y + 12}{4} = - 8$

$x = \frac{9 y}{4} + 3$

Step 5

Solve for $y$ in $\frac{11 y + 12}{4} = - 8$ .

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Step 5.1

Multiply both sides by $4$ .

$\frac{11 y + 12}{4} \cdot 4 = - 8 \cdot 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

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

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Cancel the common factor.

$\frac{11 y + 12}{4} \cdot 4 = - 8 \cdot 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.2.1.1.2

Rewrite the expression.

$11 y + 12 = - 8 \cdot 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$11 y + 12 = - 8 \cdot 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$11 y + 12 = - 8 \cdot 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Multiply $- 8$ by $4$ .

$11 y + 12 = - 32$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$11 y + 12 = - 32$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$11 y + 12 = - 32$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.3

Solve for $y$ .

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Step 5.3.1

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

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Step 5.3.1.1

Subtract $12$ from both sides of the equation.

$11 y = - 32 - 12$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.3.1.2

Subtract $12$ from $- 32$ .

$11 y = - 44$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$11 y = - 44$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.3.2

Divide each term in $11 y = - 44$ by $11$ and simplify.

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Step 5.3.2.1

Divide each term in $11 y = - 44$ by $11$ .

$\frac{11 y}{11} = \frac{- 44}{11}$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.3.2.2

Simplify the left side.

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Step 5.3.2.2.1

Cancel the common factor of $11$ .

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Step 5.3.2.2.1.1

Cancel the common factor.

$\frac{11 y}{11} = \frac{- 44}{11}$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 44}{11}$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$y = \frac{- 44}{11}$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$y = \frac{- 44}{11}$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 5.3.2.3

Simplify the right side.

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Step 5.3.2.3.1

Divide $- 44$ by $11$ .

$y = - 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$y = - 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$y = - 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$y = - 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

$y = - 4$

$z = - \frac{7 y}{4}$

$x = \frac{9 y}{4} + 3$

Step 6

Replace all occurrences of $y$ with $- 4$ in each equation.

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Step 6.1

Replace all occurrences of $y$ in $z = - \frac{7 y}{4}$ with $- 4$ .

$z = - \frac{7 (- 4)}{4}$

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{7 (- 4)}{4}$ .

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Step 6.2.1.1

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

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Step 6.2.1.1.1

Factor $4$ out of $7 (- 4)$ .

$z = - \frac{4 (7 \cdot (- 1))}{4}$

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2.1.1.2

Cancel the common factors.

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Step 6.2.1.1.2.1

Factor $4$ out of $4$ .

$z = - \frac{4 (7 \cdot (- 1))}{4 (1)}$

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2.1.1.2.2

Cancel the common factor.

$z = - \frac{4 (7 \cdot (- 1))}{4 \cdot 1}$

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2.1.1.2.3

Rewrite the expression.

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

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2.1.1.2.4

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

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

$y = - 4$

$x = \frac{9 y}{4} + 3$

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

$y = - 4$

$x = \frac{9 y}{4} + 3$

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

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2.1.2

Multiply $- (7 \cdot (- 1))$ .

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Step 6.2.1.2.1

Multiply $7$ by $- 1$ .

$z = 7$

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.2.1.2.2

Multiply $- 1$ by $- 7$ .

$z = 7$

$y = - 4$

$x = \frac{9 y}{4} + 3$

$z = 7$

$y = - 4$

$x = \frac{9 y}{4} + 3$

$z = 7$

$y = - 4$

$x = \frac{9 y}{4} + 3$

$z = 7$

$y = - 4$

$x = \frac{9 y}{4} + 3$

Step 6.3

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

$x = \frac{9 (- 4)}{4} + 3$

$z = 7$

$y = - 4$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{9 (- 4)}{4} + 3$ .

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Step 6.4.1.1

Multiply $9$ by $- 4$ .

$x = \frac{- 36}{4} + 3$

$z = 7$

$y = - 4$

Step 6.4.1.2

Divide $- 36$ by $4$ .

$x = - 9 + 3$

$z = 7$

$y = - 4$

Step 6.4.1.3

Add $- 9$ and $3$ .

$x = - 6$

$z = 7$

$y = - 4$

$x = - 6$

$z = 7$

$y = - 4$

$x = - 6$

$z = 7$

$y = - 4$

$x = - 6$

$z = 7$

$y = - 4$

Step 7

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

$(- 6, - 4, 7)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 6, - 4, 7)$

Equation Form:

$x = - 6, y = - 4, z = 7$