Finite Math Examples

$3 x + 3 y + z = 22$ , $x + z = 6$ , $4 y - 3 z = 8$

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.

$3 y + z = 22 - 3 x$

$x + z = 6$

$4 y - 3 z = 8$

Step 1.2

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

$z = 22 - 3 x - 3 y$

$x + z = 6$

$4 y - 3 z = 8$

$z = 22 - 3 x - 3 y$

$x + z = 6$

$4 y - 3 z = 8$

Step 2

Replace all occurrences of $z$ with $22 - 3 x - 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $z$ in $x + z = 6$ with $22 - 3 x - 3 y$ .

$x + 22 - 3 x - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 3 z = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x + 22 - 3 x - 3 y$ .

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Step 2.2.1.1

Remove parentheses.

$x + 22 - 3 x - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 3 z = 8$

Step 2.2.1.2

Subtract $3 x$ from $x$ .

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 3 z = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 3 z = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 3 z = 8$

Step 2.3

Replace all occurrences of $z$ in $4 y - 3 z = 8$ with $22 - 3 x - 3 y$ .

$4 y - 3 (22 - 3 x - 3 y) = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $4 y - 3 (22 - 3 x - 3 y)$ .

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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.

$4 y - 3 \cdot 22 - 3 (- 3 x) - 3 (- 3 y) = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $- 3$ by $22$ .

$4 y - 66 - 3 (- 3 x) - 3 (- 3 y) = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 2.4.1.1.2.2

Multiply $- 3$ by $- 3$ .

$4 y - 66 + 9 x - 3 (- 3 y) = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 2.4.1.1.2.3

Multiply $- 3$ by $- 3$ .

$4 y - 66 + 9 x + 9 y = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 66 + 9 x + 9 y = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$4 y - 66 + 9 x + 9 y = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 2.4.1.2

Add $4 y$ and $9 y$ .

$13 y - 66 + 9 x = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$13 y - 66 + 9 x = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$13 y - 66 + 9 x = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$13 y - 66 + 9 x = 8$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3

Solve for $y$ in $13 y - 66 + 9 x = 8$ .

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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

Add $66$ to both sides of the equation.

$13 y + 9 x = 8 + 66$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3.1.2

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

$13 y = 8 + 66 - 9 x$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3.1.3

Add $8$ and $66$ .

$13 y = 74 - 9 x$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$13 y = 74 - 9 x$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3.2

Divide each term in $13 y = 74 - 9 x$ by $13$ and simplify.

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Step 3.2.1

Divide each term in $13 y = 74 - 9 x$ by $13$ .

$\frac{13 y}{13} = \frac{74}{13} + \frac{- 9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $13$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{74}{13} + \frac{- 9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{74}{13} + \frac{- 9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$y = \frac{74}{13} + \frac{- 9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$y = \frac{74}{13} + \frac{- 9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$y = \frac{74}{13} - \frac{9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$y = \frac{74}{13} - \frac{9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$y = \frac{74}{13} - \frac{9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

$y = \frac{74}{13} - \frac{9 x}{13}$

$- 2 x + 22 - 3 y = 6$

$z = 22 - 3 x - 3 y$

Step 4

Replace all occurrences of $y$ with $\frac{74}{13} - \frac{9 x}{13}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $- 2 x + 22 - 3 y = 6$ with $\frac{74}{13} - \frac{9 x}{13}$ .

$- 2 x + 22 - 3 (\frac{74}{13} - \frac{9 x}{13}) = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- 2 x + 22 - 3 (\frac{74}{13} - \frac{9 x}{13})$ .

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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.

$- 2 x + 22 - 3 (\frac{74}{13}) - 3 (- \frac{9 x}{13}) = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.1.2

Multiply $- 3 (\frac{74}{13})$ .

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Step 4.2.1.1.2.1

Combine $- 3$ and $\frac{74}{13}$ .

$- 2 x + 22 + \frac{- 3 \cdot 74}{13} - 3 (- \frac{9 x}{13}) = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.1.2.2

Multiply $- 3$ by $74$ .

$- 2 x + 22 + \frac{- 222}{13} - 3 (- \frac{9 x}{13}) = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$- 2 x + 22 + \frac{- 222}{13} - 3 (- \frac{9 x}{13}) = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.1.3

Multiply $- 3 (- \frac{9 x}{13})$ .

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Step 4.2.1.1.3.1

Multiply $- 1$ by $- 3$ .

$- 2 x + 22 + \frac{- 222}{13} + 3 (\frac{9 x}{13}) = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.1.3.2

Combine $3$ and $\frac{9 x}{13}$ .

$- 2 x + 22 + \frac{- 222}{13} + \frac{3 (9 x)}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.1.3.3

Multiply $9$ by $3$ .

$- 2 x + 22 + \frac{- 222}{13} + \frac{27 x}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$- 2 x + 22 + \frac{- 222}{13} + \frac{27 x}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.1.4

Move the negative in front of the fraction.

$- 2 x + 22 - \frac{222}{13} + \frac{27 x}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$- 2 x + 22 - \frac{222}{13} + \frac{27 x}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$- 2 x \cdot \frac{13}{13} + \frac{27 x}{13} + 22 - \frac{222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.3

Combine $- 2 x$ and $\frac{13}{13}$ .

$\frac{- 2 x \cdot 13}{13} + \frac{27 x}{13} + 22 - \frac{222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 13 + 27 x}{13} + 22 - \frac{222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.5

Combine the numerators over the common denominator.

$22 + \frac{- 2 x \cdot 13 + 27 x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.6

Multiply $13$ by $- 2$ .

$22 + \frac{- 26 x + 27 x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.7

Add $- 26 x$ and $27 x$ .

$22 + \frac{x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.8

To write $22$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$22 \cdot \frac{13}{13} + \frac{x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.9

Simplify terms.

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Step 4.2.1.9.1

Combine $22$ and $\frac{13}{13}$ .

$\frac{22 \cdot 13}{13} + \frac{x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.9.2

Combine the numerators over the common denominator.

$\frac{22 \cdot 13 + x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$\frac{22 \cdot 13 + x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.10

Simplify the numerator.

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Step 4.2.1.10.1

Multiply $22$ by $13$ .

$\frac{286 + x - 222}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.2.1.10.2

Subtract $222$ from $286$ .

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - 3 y$

Step 4.3

Replace all occurrences of $y$ in $z = 22 - 3 x - 3 y$ with $\frac{74}{13} - \frac{9 x}{13}$ .

$z = 22 - 3 x - 3 (\frac{74}{13} - \frac{9 x}{13})$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $22 - 3 x - 3 (\frac{74}{13} - \frac{9 x}{13})$ .

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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.

$z = 22 - 3 x - 3 (\frac{74}{13}) - 3 (- \frac{9 x}{13})$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.1.2

Multiply $- 3 (\frac{74}{13})$ .

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Step 4.4.1.1.2.1

Combine $- 3$ and $\frac{74}{13}$ .

$z = 22 - 3 x + \frac{- 3 \cdot 74}{13} - 3 (- \frac{9 x}{13})$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.1.2.2

Multiply $- 3$ by $74$ .

$z = 22 - 3 x + \frac{- 222}{13} - 3 (- \frac{9 x}{13})$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x + \frac{- 222}{13} - 3 (- \frac{9 x}{13})$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.1.3

Multiply $- 3 (- \frac{9 x}{13})$ .

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 3$ .

$z = 22 - 3 x + \frac{- 222}{13} + 3 (\frac{9 x}{13})$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.1.3.2

Combine $3$ and $\frac{9 x}{13}$ .

$z = 22 - 3 x + \frac{- 222}{13} + \frac{3 (9 x)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.1.3.3

Multiply $9$ by $3$ .

$z = 22 - 3 x + \frac{- 222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x + \frac{- 222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$z = 22 - 3 x - \frac{222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = 22 - 3 x - \frac{222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.2

To write $22$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$z = - 3 x + 22 \cdot \frac{13}{13} - \frac{222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.3

Combine $22$ and $\frac{13}{13}$ .

$z = - 3 x + \frac{22 \cdot 13}{13} - \frac{222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$z = - 3 x + \frac{22 \cdot 13 - 222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $22$ by $13$ .

$z = - 3 x + \frac{286 - 222}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.5.2

Subtract $222$ from $286$ .

$z = - 3 x + \frac{64}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - 3 x + \frac{64}{13} + \frac{27 x}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.6

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$z = - 3 x \cdot \frac{13}{13} + \frac{27 x}{13} + \frac{64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.7

Combine $- 3 x$ and $\frac{13}{13}$ .

$z = \frac{- 3 x \cdot 13}{13} + \frac{27 x}{13} + \frac{64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.8

Combine the numerators over the common denominator.

$z = \frac{- 3 x \cdot 13 + 27 x}{13} + \frac{64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$z = \frac{- 3 x \cdot 13 + 27 x + 64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.10

Multiply $13$ by $- 3$ .

$z = \frac{- 39 x + 27 x + 64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.11

Add $- 39 x$ and $27 x$ .

$z = \frac{- 12 x + 64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.12

Factor $4$ out of $- 12 x + 64$ .

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Step 4.4.1.12.1

Factor $4$ out of $- 12 x$ .

$z = \frac{4 (- 3 x) + 64}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.12.2

Factor $4$ out of $64$ .

$z = \frac{4 (- 3 x) + 4 (16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.12.3

Factor $4$ out of $4 (- 3 x) + 4 (16)$ .

$z = \frac{4 (- 3 x + 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = \frac{4 (- 3 x + 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.13

Factor $- 1$ out of $- 3 x$ .

$z = \frac{4 (- (3 x) + 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.14

Rewrite $16$ as $- 1 (- 16)$ .

$z = \frac{4 (- (3 x) - 1 \cdot - 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.15

Factor $- 1$ out of $- (3 x) - 1 (- 16)$ .

$z = \frac{4 (- (3 x - 16))}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.16

Simplify the expression.

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Step 4.4.1.16.1

Rewrite $- (3 x - 16)$ as $- 1 (3 x - 16)$ .

$z = \frac{4 (- 1 (3 x - 16))}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 4.4.1.16.2

Move the negative in front of the fraction.

$z = - \frac{4 (3 x - 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - \frac{4 (3 x - 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - \frac{4 (3 x - 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - \frac{4 (3 x - 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - \frac{4 (3 x - 16)}{13}$

$\frac{x + 64}{13} = 6$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 5

Solve for $x$ in $\frac{x + 64}{13} = 6$ .

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Step 5.1

Multiply both sides of the equation by $13$ .

$13 (\frac{x + 64}{13}) = 13 \cdot 6$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 5.2

Simplify both sides of the equation.

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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 $13$ .

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Step 5.2.1.1.1

Cancel the common factor.

$13 (\frac{x + 64}{13}) = 13 \cdot 6$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 5.2.1.1.2

Rewrite the expression.

$x + 64 = 13 \cdot 6$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

$x + 64 = 13 \cdot 6$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

$x + 64 = 13 \cdot 6$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Multiply $13$ by $6$ .

$x + 64 = 78$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

$x + 64 = 78$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

$x + 64 = 78$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 5.3

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

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Step 5.3.1

Subtract $64$ from both sides of the equation.

$x = 78 - 64$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 5.3.2

Subtract $64$ from $78$ .

$x = 14$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

$x = 14$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

$x = 14$

$z = - \frac{4 (3 x - 16)}{13}$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6

Replace all occurrences of $x$ with $14$ in each equation.

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Step 6.1

Replace all occurrences of $x$ in $z = - \frac{4 (3 x - 16)}{13}$ with $14$ .

$z = - \frac{4 (3 (14) - 16)}{13}$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{4 (3 (14) - 16)}{13}$ .

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Step 6.2.1.1

Simplify the numerator.

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Step 6.2.1.1.1

Multiply $3$ by $14$ .

$z = - \frac{4 (42 - 16)}{13}$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6.2.1.1.2

Subtract $16$ from $42$ .

$z = - \frac{4 \cdot 26}{13}$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - \frac{4 \cdot 26}{13}$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6.2.1.2

Simplify the expression.

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Step 6.2.1.2.1

Multiply $4$ by $26$ .

$z = - \frac{104}{13}$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6.2.1.2.2

Divide $104$ by $13$ .

$z = - 1 \cdot 8$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6.2.1.2.3

Multiply $- 1$ by $8$ .

$z = - 8$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - 8$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - 8$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

$z = - 8$

$x = 14$

$y = \frac{74}{13} - \frac{9 x}{13}$

Step 6.3

Replace all occurrences of $x$ in $y = \frac{74}{13} - \frac{9 x}{13}$ with $14$ .

$y = \frac{74}{13} - \frac{9 (14)}{13}$

$z = - 8$

$x = 14$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{74}{13} - \frac{9 (14)}{13}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$y = \frac{74 - 9 \cdot 14}{13}$

$z = - 8$

$x = 14$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $- 9$ by $14$ .

$y = \frac{74 - 126}{13}$

$z = - 8$

$x = 14$

Step 6.4.1.2.2

Subtract $126$ from $74$ .

$y = \frac{- 52}{13}$

$z = - 8$

$x = 14$

Step 6.4.1.2.3

Divide $- 52$ by $13$ .

$y = - 4$

$z = - 8$

$x = 14$

$y = - 4$

$z = - 8$

$x = 14$

$y = - 4$

$z = - 8$

$x = 14$

$y = - 4$

$z = - 8$

$x = 14$

$y = - 4$

$z = - 8$

$x = 14$

Step 7

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

$(14, - 4, - 8)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(14, - 4, - 8)$

Equation Form:

$x = 14, y = - 4, z = - 8$