Finite Math Examples

$6 x + z = - 26$ , $1 w + 5 y - z = 26$ , $6 w + y + 5 z = 13$ , $w + x + 3 y = 14$

Step 1

Subtract $6 x$ from both sides of the equation.

$z = - 26 - 6 x$

$w + 5 y - z = 26$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

Step 2

Replace all occurrences of $z$ with $- 26 - 6 x$ in each equation.

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Step 2.1

Replace all occurrences of $z$ in $w + 5 y - z = 26$ with $- 26 - 6 x$ .

$w + 5 y - (- 26 - 6 x) = 26$

$z = - 26 - 6 x$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Apply the distributive property.

$w + 5 y + 26 - (- 6 x) = 26$

$z = - 26 - 6 x$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

Step 2.2.1.2

Multiply $- 1$ by $- 26$ .

$w + 5 y + 26 - (- 6 x) = 26$

$z = - 26 - 6 x$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

Step 2.2.1.3

Multiply $- 6$ by $- 1$ .

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$6 w + y + 5 z = 13$

$w + x + 3 y = 14$

Step 2.3

Replace all occurrences of $z$ in $6 w + y + 5 z = 13$ with $- 26 - 6 x$ .

$6 w + y + 5 (- 26 - 6 x) = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Apply the distributive property.

$6 w + y + 5 \cdot - 26 + 5 (- 6 x) = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 2.4.1.2

Multiply $5$ by $- 26$ .

$6 w + y - 130 + 5 (- 6 x) = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 2.4.1.3

Multiply $- 6$ by $5$ .

$6 w + y - 130 - 30 x = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$6 w + y - 130 - 30 x = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$6 w + y - 130 - 30 x = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$6 w + y - 130 - 30 x = 13$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 3

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

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Step 3.1

Subtract $6 w$ from both sides of the equation.

$y - 130 - 30 x = 13 - 6 w$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 3.2

Add $130$ to both sides of the equation.

$y - 30 x = 13 - 6 w + 130$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 3.3

Add $30 x$ to both sides of the equation.

$y = 13 - 6 w + 130 + 30 x$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 3.4

Add $13$ and $130$ .

$y = - 6 w + 143 + 30 x$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$y = - 6 w + 143 + 30 x$

$w + 5 y + 26 + 6 x = 26$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4

Replace all occurrences of $y$ with $- 6 w + 143 + 30 x$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $w + 5 y + 26 + 6 x = 26$ with $- 6 w + 143 + 30 x$ .

$w + 5 (- 6 w + 143 + 30 x) + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $w + 5 (- 6 w + 143 + 30 x) + 26 + 6 x$ .

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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.

$w + 5 (- 6 w) + 5 \cdot 143 + 5 (30 x) + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2.1.1.2

Simplify.

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Step 4.2.1.1.2.1

Multiply $- 6$ by $5$ .

$w - 30 w + 5 \cdot 143 + 5 (30 x) + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2.1.1.2.2

Multiply $5$ by $143$ .

$w - 30 w + 715 + 5 (30 x) + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2.1.1.2.3

Multiply $30$ by $5$ .

$w - 30 w + 715 + 150 x + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$w - 30 w + 715 + 150 x + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$w - 30 w + 715 + 150 x + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2.1.2

Simplify by adding terms.

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Step 4.2.1.2.1

Subtract $30 w$ from $w$ .

$- 29 w + 715 + 150 x + 26 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2.1.2.2

Add $715$ and $26$ .

$- 29 w + 150 x + 741 + 6 x = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.2.1.2.3

Add $150 x$ and $6 x$ .

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x + 3 y = 14$

Step 4.3

Replace all occurrences of $y$ in $w + x + 3 y = 14$ with $- 6 w + 143 + 30 x$ .

$w + x + 3 (- 6 w + 143 + 30 x) = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 4.4

Simplify the left side.

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Step 4.4.1

Simplify $w + x + 3 (- 6 w + 143 + 30 x)$ .

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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.

$w + x + 3 (- 6 w) + 3 \cdot 143 + 3 (30 x) = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 4.4.1.1.2

Simplify.

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Step 4.4.1.1.2.1

Multiply $- 6$ by $3$ .

$w + x - 18 w + 3 \cdot 143 + 3 (30 x) = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 4.4.1.1.2.2

Multiply $3$ by $143$ .

$w + x - 18 w + 429 + 3 (30 x) = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 4.4.1.1.2.3

Multiply $30$ by $3$ .

$w + x - 18 w + 429 + 90 x = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x - 18 w + 429 + 90 x = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$w + x - 18 w + 429 + 90 x = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 4.4.1.2

Simplify by adding terms.

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Step 4.4.1.2.1

Subtract $18 w$ from $w$ .

$- 17 w + x + 429 + 90 x = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 4.4.1.2.2

Add $x$ and $90 x$ .

$- 17 w + 91 x + 429 = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$- 17 w + 91 x + 429 = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$- 17 w + 91 x + 429 = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$- 17 w + 91 x + 429 = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

$- 17 w + 91 x + 429 = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$z = - 26 - 6 x$

Step 5

Reorder $- 26$ and $- 6 x$ .

$z = - 6 x - 26$

$- 17 w + 91 x + 429 = 14$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6

Solve for $w$ in $- 17 w + 91 x + 429 = 14$ .

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Step 6.1

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

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Step 6.1.1

Subtract $91 x$ from both sides of the equation.

$- 17 w + 429 = 14 - 91 x$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.1.2

Subtract $429$ from both sides of the equation.

$- 17 w = 14 - 91 x - 429$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.1.3

Subtract $429$ from $14$ .

$- 17 w = - 91 x - 415$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$- 17 w = - 91 x - 415$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.2

Divide each term in $- 17 w = - 91 x - 415$ by $- 17$ and simplify.

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Step 6.2.1

Divide each term in $- 17 w = - 91 x - 415$ by $- 17$ .

$\frac{- 17 w}{- 17} = \frac{- 91 x}{- 17} + \frac{- 415}{- 17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $- 17$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{- 17 w}{- 17} = \frac{- 91 x}{- 17} + \frac{- 415}{- 17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 91 x}{- 17} + \frac{- 415}{- 17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$w = \frac{- 91 x}{- 17} + \frac{- 415}{- 17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$w = \frac{- 91 x}{- 17} + \frac{- 415}{- 17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Simplify each term.

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Step 6.2.3.1.1

Dividing two negative values results in a positive value.

$w = \frac{91 x}{17} + \frac{- 415}{- 17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 6.2.3.1.2

Dividing two negative values results in a positive value.

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$- 29 w + 156 x + 741 = 26$

$y = - 6 w + 143 + 30 x$

Step 7

Replace all occurrences of $w$ with $\frac{91 x}{17} + \frac{415}{17}$ in each equation.

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Step 7.1

Replace all occurrences of $w$ in $- 29 w + 156 x + 741 = 26$ with $\frac{91 x}{17} + \frac{415}{17}$ .

$- 29 (\frac{91 x}{17} + \frac{415}{17}) + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2

Simplify the left side.

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Step 7.2.1

Simplify $- 29 (\frac{91 x}{17} + \frac{415}{17}) + 156 x + 741$ .

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Step 7.2.1.1

Simplify each term.

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Step 7.2.1.1.1

Apply the distributive property.

$- 29 \frac{91 x}{17} - 29 (\frac{415}{17}) + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.1.2

Multiply $- 29 \frac{91 x}{17}$ .

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Step 7.2.1.1.2.1

Combine $- 29$ and $\frac{91 x}{17}$ .

$\frac{- 29 (91 x)}{17} - 29 (\frac{415}{17}) + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.1.2.2

Multiply $91$ by $- 29$ .

$\frac{- 2639 x}{17} - 29 (\frac{415}{17}) + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$\frac{- 2639 x}{17} - 29 (\frac{415}{17}) + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.1.3

Multiply $- 29 (\frac{415}{17})$ .

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Step 7.2.1.1.3.1

Combine $- 29$ and $\frac{415}{17}$ .

$\frac{- 2639 x}{17} + \frac{- 29 \cdot 415}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.1.3.2

Multiply $- 29$ by $415$ .

$\frac{- 2639 x}{17} + \frac{- 12035}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$\frac{- 2639 x}{17} + \frac{- 12035}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.1.4

Simplify each term.

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Step 7.2.1.1.4.1

Move the negative in front of the fraction.

$- \frac{2639 x}{17} + \frac{- 12035}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.1.4.2

Move the negative in front of the fraction.

$- \frac{2639 x}{17} - \frac{12035}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$- \frac{2639 x}{17} - \frac{12035}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$- \frac{2639 x}{17} - \frac{12035}{17} + 156 x + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.2

To write $156 x$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$- \frac{2639 x}{17} + 156 x \cdot \frac{17}{17} - \frac{12035}{17} + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.3

Combine $156 x$ and $\frac{17}{17}$ .

$- \frac{2639 x}{17} + \frac{156 x \cdot 17}{17} - \frac{12035}{17} + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.4

Combine the numerators over the common denominator.

$\frac{- 2639 x + 156 x \cdot 17}{17} - \frac{12035}{17} + 741 = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.5

Combine the numerators over the common denominator.

$741 + \frac{- 2639 x + 156 x \cdot 17 - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.6

Multiply $17$ by $156$ .

$741 + \frac{- 2639 x + 2652 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.7

Add $- 2639 x$ and $2652 x$ .

$741 + \frac{13 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.8

To write $741$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$741 \cdot \frac{17}{17} + \frac{13 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.9

Simplify terms.

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Step 7.2.1.9.1

Combine $741$ and $\frac{17}{17}$ .

$\frac{741 \cdot 17}{17} + \frac{13 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.9.2

Combine the numerators over the common denominator.

$\frac{741 \cdot 17 + 13 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$\frac{741 \cdot 17 + 13 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.10

Simplify the numerator.

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Step 7.2.1.10.1

Multiply $741$ by $17$ .

$\frac{12597 + 13 x - 12035}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.2.1.10.2

Subtract $12035$ from $12597$ .

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - 6 w + 143 + 30 x$

Step 7.3

Replace all occurrences of $w$ in $y = - 6 w + 143 + 30 x$ with $\frac{91 x}{17} + \frac{415}{17}$ .

$y = - 6 (\frac{91 x}{17} + \frac{415}{17}) + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4

Simplify the right side.

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Step 7.4.1

Simplify $- 6 (\frac{91 x}{17} + \frac{415}{17}) + 143 + 30 x$ .

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Step 7.4.1.1

Simplify each term.

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Step 7.4.1.1.1

Apply the distributive property.

$y = - 6 \frac{91 x}{17} - 6 (\frac{415}{17}) + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.1.2

Multiply $- 6 \frac{91 x}{17}$ .

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Step 7.4.1.1.2.1

Combine $- 6$ and $\frac{91 x}{17}$ .

$y = \frac{- 6 (91 x)}{17} - 6 (\frac{415}{17}) + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.1.2.2

Multiply $91$ by $- 6$ .

$y = \frac{- 546 x}{17} - 6 (\frac{415}{17}) + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{- 546 x}{17} - 6 (\frac{415}{17}) + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.1.3

Multiply $- 6 (\frac{415}{17})$ .

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Step 7.4.1.1.3.1

Combine $- 6$ and $\frac{415}{17}$ .

$y = \frac{- 546 x}{17} + \frac{- 6 \cdot 415}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.1.3.2

Multiply $- 6$ by $415$ .

$y = \frac{- 546 x}{17} + \frac{- 2490}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{- 546 x}{17} + \frac{- 2490}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.1.4

Simplify each term.

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Step 7.4.1.1.4.1

Move the negative in front of the fraction.

$y = - \frac{546 x}{17} + \frac{- 2490}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.1.4.2

Move the negative in front of the fraction.

$y = - \frac{546 x}{17} - \frac{2490}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{546 x}{17} - \frac{2490}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{546 x}{17} - \frac{2490}{17} + 143 + 30 x$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.2

To write $30 x$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$y = - \frac{546 x}{17} + 30 x \cdot \frac{17}{17} - \frac{2490}{17} + 143$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.3

Combine $30 x$ and $\frac{17}{17}$ .

$y = - \frac{546 x}{17} + \frac{30 x \cdot 17}{17} - \frac{2490}{17} + 143$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.4

Combine the numerators over the common denominator.

$y = \frac{- 546 x + 30 x \cdot 17}{17} - \frac{2490}{17} + 143$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.5

Combine the numerators over the common denominator.

$y = 143 + \frac{- 546 x + 30 x \cdot 17 - 2490}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.6

Multiply $17$ by $30$ .

$y = 143 + \frac{- 546 x + 510 x - 2490}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.7

Add $- 546 x$ and $510 x$ .

$y = 143 + \frac{- 36 x - 2490}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.8

Factor $6$ out of $- 36 x - 2490$ .

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Step 7.4.1.8.1

Factor $6$ out of $- 36 x$ .

$y = 143 + \frac{6 (- 6 x) - 2490}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.8.2

Factor $6$ out of $- 2490$ .

$y = 143 + \frac{6 (- 6 x) + 6 (- 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.8.3

Factor $6$ out of $6 (- 6 x) + 6 (- 415)$ .

$y = 143 + \frac{6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = 143 + \frac{6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.9

To write $143$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$y = 143 \cdot \frac{17}{17} + \frac{6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.10

Simplify terms.

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Step 7.4.1.10.1

Combine $143$ and $\frac{17}{17}$ .

$y = \frac{143 \cdot 17}{17} + \frac{6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.10.2

Combine the numerators over the common denominator.

$y = \frac{143 \cdot 17 + 6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{143 \cdot 17 + 6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.11

Simplify the numerator.

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Step 7.4.1.11.1

Multiply $143$ by $17$ .

$y = \frac{2431 + 6 (- 6 x - 415)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.11.2

Apply the distributive property.

$y = \frac{2431 + 6 (- 6 x) + 6 \cdot - 415}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.11.3

Multiply $- 6$ by $6$ .

$y = \frac{2431 - 36 x + 6 \cdot - 415}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.11.4

Multiply $6$ by $- 415$ .

$y = \frac{2431 - 36 x - 2490}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.11.5

Subtract $2490$ from $2431$ .

$y = \frac{- 36 x - 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{- 36 x - 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.12

Simplify with factoring out.

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Step 7.4.1.12.1

Factor $- 1$ out of $- 36 x$ .

$y = \frac{- (36 x) - 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.12.2

Rewrite $- 59$ as $- 1 (59)$ .

$y = \frac{- (36 x) - 1 \cdot 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.12.3

Factor $- 1$ out of $- (36 x) - 1 (59)$ .

$y = \frac{- (36 x + 59)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.12.4

Simplify the expression.

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Step 7.4.1.12.4.1

Rewrite $- (36 x + 59)$ as $- 1 (36 x + 59)$ .

$y = \frac{- 1 (36 x + 59)}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 7.4.1.12.4.2

Move the negative in front of the fraction.

$y = - \frac{36 x + 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{36 x + 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{36 x + 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{36 x + 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{36 x + 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{36 x + 59}{17}$

$\frac{13 x + 562}{17} = 26$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8

Solve for $x$ in $\frac{13 x + 562}{17} = 26$ .

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Step 8.1

Multiply both sides by $17$ .

$\frac{13 x + 562}{17} \cdot 17 = 26 \cdot 17$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.2

Simplify.

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Step 8.2.1

Simplify the left side.

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Step 8.2.1.1

Cancel the common factor of $17$ .

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Step 8.2.1.1.1

Cancel the common factor.

$\frac{13 x + 562}{17} \cdot 17 = 26 \cdot 17$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.2.1.1.2

Rewrite the expression.

$13 x + 562 = 26 \cdot 17$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$13 x + 562 = 26 \cdot 17$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$13 x + 562 = 26 \cdot 17$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.2.2

Simplify the right side.

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Step 8.2.2.1

Multiply $26$ by $17$ .

$13 x + 562 = 442$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$13 x + 562 = 442$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$13 x + 562 = 442$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.3

Solve for $x$ .

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Step 8.3.1

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

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Step 8.3.1.1

Subtract $562$ from both sides of the equation.

$13 x = 442 - 562$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.3.1.2

Subtract $562$ from $442$ .

$13 x = - 120$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$13 x = - 120$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.3.2

Divide each term in $13 x = - 120$ by $13$ and simplify.

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Step 8.3.2.1

Divide each term in $13 x = - 120$ by $13$ .

$\frac{13 x}{13} = \frac{- 120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.3.2.2

Simplify the left side.

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Step 8.3.2.2.1

Cancel the common factor of $13$ .

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Step 8.3.2.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{- 120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$x = \frac{- 120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$x = \frac{- 120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 8.3.2.3

Simplify the right side.

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Step 8.3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$x = - \frac{120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$x = - \frac{120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$x = - \frac{120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$x = - \frac{120}{13}$

$y = - \frac{36 x + 59}{17}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9

Replace all occurrences of $x$ with $- \frac{120}{13}$ in each equation.

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Step 9.1

Replace all occurrences of $x$ in $y = - \frac{36 x + 59}{17}$ with $- \frac{120}{13}$ .

$y = - \frac{36 (- \frac{120}{13}) + 59}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2

Simplify the right side.

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Step 9.2.1

Simplify $- \frac{36 (- \frac{120}{13}) + 59}{17}$ .

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Step 9.2.1.1

Simplify the numerator.

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Step 9.2.1.1.1

Multiply $36 (- \frac{120}{13})$ .

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Step 9.2.1.1.1.1

Multiply $- 1$ by $36$ .

$y = - \frac{- 36 (\frac{120}{13}) + 59}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.1.2

Combine $- 36$ and $\frac{120}{13}$ .

$y = - \frac{\frac{- 36 \cdot 120}{13} + 59}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.1.3

Multiply $- 36$ by $120$ .

$y = - \frac{\frac{- 4320}{13} + 59}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{\frac{- 4320}{13} + 59}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.2

Move the negative in front of the fraction.

$y = - \frac{- \frac{4320}{13} + 59}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.3

To write $59$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = - \frac{- \frac{4320}{13} + 59 \cdot \frac{13}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.4

Combine $59$ and $\frac{13}{13}$ .

$y = - \frac{- \frac{4320}{13} + \frac{59 \cdot 13}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.5

Combine the numerators over the common denominator.

$y = - \frac{\frac{- 4320 + 59 \cdot 13}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.6

Simplify the numerator.

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Step 9.2.1.1.6.1

Multiply $59$ by $13$ .

$y = - \frac{\frac{- 4320 + 767}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.6.2

Add $- 4320$ and $767$ .

$y = - \frac{\frac{- 3553}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{\frac{- 3553}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.1.7

Move the negative in front of the fraction.

$y = - \frac{- \frac{3553}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{- \frac{3553}{13}}{17}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = - (- \frac{3553}{13} \cdot \frac{1}{17})$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.3

Cancel the common factor of $17$ .

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Step 9.2.1.3.1

Move the leading negative in $- \frac{3553}{13}$ into the numerator.

$y = - (\frac{- 3553}{13} \cdot \frac{1}{17})$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.3.2

Factor $17$ out of $- 3553$ .

$y = - (\frac{17 (- 209)}{13} \cdot \frac{1}{17})$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.3.3

Cancel the common factor.

$y = - (\frac{17 \cdot - 209}{13} \cdot \frac{1}{17})$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.3.4

Rewrite the expression.

$y = - \frac{- 209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = - \frac{- 209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.4

Move the negative in front of the fraction.

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.5

Multiply $- - \frac{209}{13}$ .

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Step 9.2.1.5.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{209}{13})$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.2.1.5.2

Multiply $\frac{209}{13}$ by $1$ .

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$w = \frac{91 x}{17} + \frac{415}{17}$

$z = - 6 x - 26$

Step 9.3

Replace all occurrences of $x$ in $w = \frac{91 x}{17} + \frac{415}{17}$ with $- \frac{120}{13}$ .

$w = \frac{91 (- \frac{120}{13})}{17} + \frac{415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4

Simplify the right side.

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Step 9.4.1

Simplify $\frac{91 (- \frac{120}{13})}{17} + \frac{415}{17}$ .

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Step 9.4.1.1

Combine the numerators over the common denominator.

$w = \frac{91 (- \frac{120}{13}) + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.2

Simplify each term.

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Step 9.4.1.2.1

Cancel the common factor of $13$ .

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Step 9.4.1.2.1.1

Move the leading negative in $- \frac{120}{13}$ into the numerator.

$w = \frac{91 (\frac{- 120}{13}) + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.2.1.2

Factor $13$ out of $91$ .

$w = \frac{13 (7) (\frac{- 120}{13}) + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.2.1.3

Cancel the common factor.

$w = \frac{13 \cdot (7 (\frac{- 120}{13})) + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.2.1.4

Rewrite the expression.

$w = \frac{7 \cdot - 120 + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

$w = \frac{7 \cdot - 120 + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.2.2

Multiply $7$ by $- 120$ .

$w = \frac{- 840 + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

$w = \frac{- 840 + 415}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.3

Simplify the expression.

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Step 9.4.1.3.1

Add $- 840$ and $415$ .

$w = \frac{- 425}{17}$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.4.1.3.2

Divide $- 425$ by $17$ .

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = - 6 x - 26$

Step 9.5

Replace all occurrences of $x$ in $z = - 6 x - 26$ with $- \frac{120}{13}$ .

$z = - 6 (- \frac{120}{13}) - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6

Simplify the right side.

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Step 9.6.1

Simplify $- 6 (- \frac{120}{13}) - 26$ .

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Step 9.6.1.1

Multiply $- 6 (- \frac{120}{13})$ .

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Step 9.6.1.1.1

Multiply $- 1$ by $- 6$ .

$z = 6 (\frac{120}{13}) - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.1.2

Combine $6$ and $\frac{120}{13}$ .

$z = \frac{6 \cdot 120}{13} - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.1.3

Multiply $6$ by $120$ .

$z = \frac{720}{13} - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = \frac{720}{13} - 26$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.2

To write $- 26$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$z = \frac{720}{13} - 26 \cdot \frac{13}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.3

Combine $- 26$ and $\frac{13}{13}$ .

$z = \frac{720}{13} + \frac{- 26 \cdot 13}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.4

Combine the numerators over the common denominator.

$z = \frac{720 - 26 \cdot 13}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.5

Simplify the numerator.

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Step 9.6.1.5.1

Multiply $- 26$ by $13$ .

$z = \frac{720 - 338}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 9.6.1.5.2

Subtract $338$ from $720$ .

$z = \frac{382}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = \frac{382}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = \frac{382}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = \frac{382}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

$z = \frac{382}{13}$

$w = - 25$

$y = \frac{209}{13}$

$x = - \frac{120}{13}$

Step 10

List all of the solutions.

$z = \frac{382}{13}, w = - 25, y = \frac{209}{13}, x = - \frac{120}{13}$