Algebra Examples

$9 x - 4 y - 5 z = 9$ $7 x + 4 y - 4 z = - 1$ $6 x - 6 y + z = - 5$

Step 1

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

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Step 1.1

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

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

$9 x - 4 y - 5 z = 9$

$7 x + 4 y - 4 z = - 1$

Step 1.2

Add $6 y$ to both sides of the equation.

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

$9 x - 4 y - 5 z = 9$

$7 x + 4 y - 4 z = - 1$

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

$9 x - 4 y - 5 z = 9$

$7 x + 4 y - 4 z = - 1$

Step 2

Replace all occurrences of $z$ with $- 5 - 6 x + 6 y$ in each equation.

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Step 2.1

Replace all occurrences of $z$ in $9 x - 4 y - 5 z = 9$ with $- 5 - 6 x + 6 y$ .

$9 x - 4 y - 5 (- 5 - 6 x + 6 y) = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $9 x - 4 y - 5 (- 5 - 6 x + 6 y)$ .

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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.

$9 x - 4 y - 5 \cdot - 5 - 5 (- 6 x) - 5 (6 y) = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $- 5$ by $- 5$ .

$9 x - 4 y + 25 - 5 (- 6 x) - 5 (6 y) = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.2.1.1.2.2

Multiply $- 6$ by $- 5$ .

$9 x - 4 y + 25 + 30 x - 5 (6 y) = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.2.1.1.2.3

Multiply $6$ by $- 5$ .

$9 x - 4 y + 25 + 30 x - 30 y = 9$

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

$7 x + 4 y - 4 z = - 1$

$9 x - 4 y + 25 + 30 x - 30 y = 9$

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

$7 x + 4 y - 4 z = - 1$

$9 x - 4 y + 25 + 30 x - 30 y = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $9 x$ and $30 x$ .

$39 x - 4 y + 25 - 30 y = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.2.1.2.2

Subtract $30 y$ from $- 4 y$ .

$39 x - 34 y + 25 = 9$

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

$7 x + 4 y - 4 z = - 1$

$39 x - 34 y + 25 = 9$

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

$7 x + 4 y - 4 z = - 1$

$39 x - 34 y + 25 = 9$

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

$7 x + 4 y - 4 z = - 1$

$39 x - 34 y + 25 = 9$

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

$7 x + 4 y - 4 z = - 1$

Step 2.3

Replace all occurrences of $z$ in $7 x + 4 y - 4 z = - 1$ with $- 5 - 6 x + 6 y$ .

$7 x + 4 y - 4 (- 5 - 6 x + 6 y) = - 1$

$39 x - 34 y + 25 = 9$

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

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $7 x + 4 y - 4 (- 5 - 6 x + 6 y)$ .

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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.

$7 x + 4 y - 4 \cdot - 5 - 4 (- 6 x) - 4 (6 y) = - 1$

$39 x - 34 y + 25 = 9$

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

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $- 4$ by $- 5$ .

$7 x + 4 y + 20 - 4 (- 6 x) - 4 (6 y) = - 1$

$39 x - 34 y + 25 = 9$

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

Step 2.4.1.1.2.2

Multiply $- 6$ by $- 4$ .

$7 x + 4 y + 20 + 24 x - 4 (6 y) = - 1$

$39 x - 34 y + 25 = 9$

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

Step 2.4.1.1.2.3

Multiply $6$ by $- 4$ .

$7 x + 4 y + 20 + 24 x - 24 y = - 1$

$39 x - 34 y + 25 = 9$

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

$7 x + 4 y + 20 + 24 x - 24 y = - 1$

$39 x - 34 y + 25 = 9$

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

$7 x + 4 y + 20 + 24 x - 24 y = - 1$

$39 x - 34 y + 25 = 9$

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

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $7 x$ and $24 x$ .

$31 x + 4 y + 20 - 24 y = - 1$

$39 x - 34 y + 25 = 9$

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

Step 2.4.1.2.2

Subtract $24 y$ from $4 y$ .

$31 x - 20 y + 20 = - 1$

$39 x - 34 y + 25 = 9$

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

$31 x - 20 y + 20 = - 1$

$39 x - 34 y + 25 = 9$

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

$31 x - 20 y + 20 = - 1$

$39 x - 34 y + 25 = 9$

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

$31 x - 20 y + 20 = - 1$

$39 x - 34 y + 25 = 9$

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

$31 x - 20 y + 20 = - 1$

$39 x - 34 y + 25 = 9$

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

Step 3

Solve for $x$ in $31 x - 20 y + 20 = - 1$ .

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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

Add $20 y$ to both sides of the equation.

$31 x + 20 = - 1 + 20 y$

$39 x - 34 y + 25 = 9$

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

Step 3.1.2

Subtract $20$ from both sides of the equation.

$31 x = - 1 + 20 y - 20$

$39 x - 34 y + 25 = 9$

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

Step 3.1.3

Subtract $20$ from $- 1$ .

$31 x = 20 y - 21$

$39 x - 34 y + 25 = 9$

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

$31 x = 20 y - 21$

$39 x - 34 y + 25 = 9$

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

Step 3.2

Divide each term in $31 x = 20 y - 21$ by $31$ and simplify.

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Step 3.2.1

Divide each term in $31 x = 20 y - 21$ by $31$ .

$\frac{31 x}{31} = \frac{20 y}{31} + \frac{- 21}{31}$

$39 x - 34 y + 25 = 9$

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $31$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{31 x}{31} = \frac{20 y}{31} + \frac{- 21}{31}$

$39 x - 34 y + 25 = 9$

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{20 y}{31} + \frac{- 21}{31}$

$39 x - 34 y + 25 = 9$

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

$x = \frac{20 y}{31} + \frac{- 21}{31}$

$39 x - 34 y + 25 = 9$

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

$x = \frac{20 y}{31} + \frac{- 21}{31}$

$39 x - 34 y + 25 = 9$

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

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.

$x = \frac{20 y}{31} - \frac{21}{31}$

$39 x - 34 y + 25 = 9$

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

$x = \frac{20 y}{31} - \frac{21}{31}$

$39 x - 34 y + 25 = 9$

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

$x = \frac{20 y}{31} - \frac{21}{31}$

$39 x - 34 y + 25 = 9$

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

$x = \frac{20 y}{31} - \frac{21}{31}$

$39 x - 34 y + 25 = 9$

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

Step 4

Replace all occurrences of $x$ with $\frac{20 y}{31} - \frac{21}{31}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $39 x - 34 y + 25 = 9$ with $\frac{20 y}{31} - \frac{21}{31}$ .

$39 (\frac{20 y}{31} - \frac{21}{31}) - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $39 (\frac{20 y}{31} - \frac{21}{31}) - 34 y + 25$ .

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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.

$39 (\frac{20 y}{31}) + 39 (- \frac{21}{31}) - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.1.2

Multiply $39 \frac{20 y}{31}$ .

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Step 4.2.1.1.2.1

Combine $39$ and $\frac{20 y}{31}$ .

$\frac{39 (20 y)}{31} + 39 (- \frac{21}{31}) - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.1.2.2

Multiply $20$ by $39$ .

$\frac{780 y}{31} + 39 (- \frac{21}{31}) - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$\frac{780 y}{31} + 39 (- \frac{21}{31}) - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.1.3

Multiply $39 (- \frac{21}{31})$ .

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Step 4.2.1.1.3.1

Multiply $- 1$ by $39$ .

$\frac{780 y}{31} - 39 (\frac{21}{31}) - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.1.3.2

Combine $- 39$ and $\frac{21}{31}$ .

$\frac{780 y}{31} + \frac{- 39 \cdot 21}{31} - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.1.3.3

Multiply $- 39$ by $21$ .

$\frac{780 y}{31} + \frac{- 819}{31} - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$\frac{780 y}{31} + \frac{- 819}{31} - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.1.4

Move the negative in front of the fraction.

$\frac{780 y}{31} - \frac{819}{31} - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$\frac{780 y}{31} - \frac{819}{31} - 34 y + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.2

To write $- 34 y$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$\frac{780 y}{31} - 34 y \cdot \frac{31}{31} - \frac{819}{31} + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.3

Combine $- 34 y$ and $\frac{31}{31}$ .

$\frac{780 y}{31} + \frac{- 34 y \cdot 31}{31} - \frac{819}{31} + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{780 y - 34 y \cdot 31}{31} - \frac{819}{31} + 25 = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.5

Combine the numerators over the common denominator.

$25 + \frac{780 y - 34 y \cdot 31 - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.6

Multiply $31$ by $- 34$ .

$25 + \frac{780 y - 1054 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.7

Subtract $1054 y$ from $780 y$ .

$25 + \frac{- 274 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.8

To write $25$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$25 \cdot \frac{31}{31} + \frac{- 274 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.9

Simplify terms.

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Step 4.2.1.9.1

Combine $25$ and $\frac{31}{31}$ .

$\frac{25 \cdot 31}{31} + \frac{- 274 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.9.2

Combine the numerators over the common denominator.

$\frac{25 \cdot 31 - 274 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$\frac{25 \cdot 31 - 274 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.10

Simplify the numerator.

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Step 4.2.1.10.1

Multiply $25$ by $31$ .

$\frac{775 - 274 y - 819}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.10.2

Subtract $819$ from $775$ .

$\frac{- 274 y - 44}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.10.3

Factor $2$ out of $- 274 y - 44$ .

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Step 4.2.1.10.3.1

Factor $2$ out of $- 274 y$ .

$\frac{2 (- 137 y) - 44}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.10.3.2

Factor $2$ out of $- 44$ .

$\frac{2 (- 137 y) + 2 (- 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.10.3.3

Factor $2$ out of $2 (- 137 y) + 2 (- 22)$ .

$\frac{2 (- 137 y - 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$\frac{2 (- 137 y - 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$\frac{2 (- 137 y - 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.11

Simplify with factoring out.

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Step 4.2.1.11.1

Factor $- 1$ out of $- 137 y$ .

$\frac{2 (- (137 y) - 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.11.2

Rewrite $- 22$ as $- 1 (22)$ .

$\frac{2 (- (137 y) - 1 \cdot 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.11.3

Factor $- 1$ out of $- (137 y) - 1 (22)$ .

$\frac{2 (- (137 y + 22))}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.11.4

Simplify the expression.

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Step 4.2.1.11.4.1

Rewrite $- (137 y + 22)$ as $- 1 (137 y + 22)$ .

$\frac{2 (- 1 (137 y + 22))}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.2.1.11.4.2

Move the negative in front of the fraction.

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Step 4.3

Replace all occurrences of $x$ in $z = - 5 - 6 x + 6 y$ with $\frac{20 y}{31} - \frac{21}{31}$ .

$z = - 5 - 6 (\frac{20 y}{31} - \frac{21}{31}) + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $- 5 - 6 (\frac{20 y}{31} - \frac{21}{31}) + 6 y$ .

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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.

$z = - 5 - 6 \frac{20 y}{31} - 6 (- \frac{21}{31}) + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.1.2

Multiply $- 6 \frac{20 y}{31}$ .

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Step 4.4.1.1.2.1

Combine $- 6$ and $\frac{20 y}{31}$ .

$z = - 5 + \frac{- 6 (20 y)}{31} - 6 (- \frac{21}{31}) + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.1.2.2

Multiply $20$ by $- 6$ .

$z = - 5 + \frac{- 120 y}{31} - 6 (- \frac{21}{31}) + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = - 5 + \frac{- 120 y}{31} - 6 (- \frac{21}{31}) + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.1.3

Multiply $- 6 (- \frac{21}{31})$ .

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 6$ .

$z = - 5 + \frac{- 120 y}{31} + 6 (\frac{21}{31}) + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.1.3.2

Combine $6$ and $\frac{21}{31}$ .

$z = - 5 + \frac{- 120 y}{31} + \frac{6 \cdot 21}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.1.3.3

Multiply $6$ by $21$ .

$z = - 5 + \frac{- 120 y}{31} + \frac{126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = - 5 + \frac{- 120 y}{31} + \frac{126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$z = - 5 - \frac{120 y}{31} + \frac{126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = - 5 - \frac{120 y}{31} + \frac{126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$z = - \frac{120 y}{31} - 5 \cdot \frac{31}{31} + \frac{126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.3

Combine $- 5$ and $\frac{31}{31}$ .

$z = - \frac{120 y}{31} + \frac{- 5 \cdot 31}{31} + \frac{126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$z = - \frac{120 y}{31} + \frac{- 5 \cdot 31 + 126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $- 5$ by $31$ .

$z = - \frac{120 y}{31} + \frac{- 155 + 126}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.5.2

Add $- 155$ and $126$ .

$z = - \frac{120 y}{31} + \frac{- 29}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = - \frac{120 y}{31} + \frac{- 29}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.6

Move the negative in front of the fraction.

$z = - \frac{120 y}{31} - \frac{29}{31} + 6 y$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.7

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$z = - \frac{120 y}{31} + 6 y \cdot \frac{31}{31} - \frac{29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.8

Combine $6 y$ and $\frac{31}{31}$ .

$z = - \frac{120 y}{31} + \frac{6 y \cdot 31}{31} - \frac{29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$z = \frac{- 120 y + 6 y \cdot 31}{31} - \frac{29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.10

Combine the numerators over the common denominator.

$z = \frac{- 120 y + 6 y \cdot 31 - 29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.11

Multiply $31$ by $6$ .

$z = \frac{- 120 y + 186 y - 29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 4.4.1.12

Add $- 120 y$ and $186 y$ .

$z = \frac{66 y - 29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{66 y - 29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{66 y - 29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{66 y - 29}{31}$

$- \frac{2 (137 y + 22)}{31} = 9$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5

Solve for $y$ in $- \frac{2 (137 y + 22)}{31} = 9$ .

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Step 5.1

Multiply both sides of the equation by $- \frac{31}{2}$ .

$- \frac{31}{2} \cdot (- \frac{2 (137 y + 22)}{31}) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

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

Simplify $- \frac{31}{2} (- \frac{2 (137 y + 22)}{31})$ .

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Step 5.2.1.1.1

Cancel the common factor of $31$ .

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Step 5.2.1.1.1.1

Move the leading negative in $- \frac{31}{2}$ into the numerator.

$\frac{- 31}{2} \cdot (- \frac{2 (137 y + 22)}{31}) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.1.2

Move the leading negative in $- \frac{2 (137 y + 22)}{31}$ into the numerator.

$\frac{- 31}{2} \cdot \frac{- 2 (137 y + 22)}{31} = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.1.3

Factor $31$ out of $- 31$ .

$\frac{31 (- 1)}{2} \cdot \frac{- 2 (137 y + 22)}{31} = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.1.4

Cancel the common factor.

$\frac{31 \cdot - 1}{2} \cdot \frac{- 2 (137 y + 22)}{31} = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} \cdot (- 2 (137 y + 22)) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$\frac{- 1}{2} \cdot (- 2 (137 y + 22)) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.2

Cancel the common factor of $2$ .

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Step 5.2.1.1.2.1

Factor $2$ out of $- 2 (137 y + 22)$ .

$\frac{- 1}{2} \cdot (2 (- (137 y + 22))) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 (- (137 y + 22))) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.2.3

Rewrite the expression.

$137 y + 22 = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.3

Multiply.

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Step 5.2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (137 y + 22) = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.1.1.3.2

Multiply $137 y + 22$ by $1$ .

$137 y + 22 = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{31}{2} \cdot 9$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Simplify $- \frac{31}{2} \cdot 9$ .

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Step 5.2.2.1.1

Multiply $- \frac{31}{2} \cdot 9$ .

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Step 5.2.2.1.1.1

Multiply $9$ by $- 1$ .

$137 y + 22 = - 9 (\frac{31}{2})$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.2.1.1.2

Combine $- 9$ and $\frac{31}{2}$ .

$137 y + 22 = \frac{- 9 \cdot 31}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.2.1.1.3

Multiply $- 9$ by $31$ .

$137 y + 22 = \frac{- 279}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = \frac{- 279}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.2.2.1.2

Move the negative in front of the fraction.

$137 y + 22 = - \frac{279}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{279}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{279}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y + 22 = - \frac{279}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3

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

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Step 5.3.1

Subtract $22$ from both sides of the equation.

$137 y = - \frac{279}{2} - 22$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3.2

To write $- 22$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$137 y = - \frac{279}{2} - 22 \cdot \frac{2}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3.3

Combine $- 22$ and $\frac{2}{2}$ .

$137 y = - \frac{279}{2} + \frac{- 22 \cdot 2}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3.4

Combine the numerators over the common denominator.

$137 y = \frac{- 279 - 22 \cdot 2}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3.5

Simplify the numerator.

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Step 5.3.5.1

Multiply $- 22$ by $2$ .

$137 y = \frac{- 279 - 44}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3.5.2

Subtract $44$ from $- 279$ .

$137 y = \frac{- 323}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y = \frac{- 323}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.3.6

Move the negative in front of the fraction.

$137 y = - \frac{323}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$137 y = - \frac{323}{2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.4

Divide each term in $137 y = - \frac{323}{2}$ by $137$ and simplify.

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Step 5.4.1

Divide each term in $137 y = - \frac{323}{2}$ by $137$ .

$\frac{137 y}{137} = \frac{- \frac{323}{2}}{137}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $137$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{137 y}{137} = \frac{- \frac{323}{2}}{137}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{323}{2}}{137}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$y = \frac{- \frac{323}{2}}{137}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$y = \frac{- \frac{323}{2}}{137}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{323}{2} \cdot \frac{1}{137}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.4.3.2

Multiply $- \frac{323}{2} \cdot \frac{1}{137}$ .

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Step 5.4.3.2.1

Multiply $\frac{1}{137}$ by $\frac{323}{2}$ .

$y = - \frac{323}{137 \cdot 2}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 5.4.3.2.2

Multiply $137$ by $2$ .

$y = - \frac{323}{274}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$y = - \frac{323}{274}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$y = - \frac{323}{274}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$y = - \frac{323}{274}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$y = - \frac{323}{274}$

$z = \frac{66 y - 29}{31}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6

Replace all occurrences of $y$ with $- \frac{323}{274}$ in each equation.

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Step 6.1

Replace all occurrences of $y$ in $z = \frac{66 y - 29}{31}$ with $- \frac{323}{274}$ .

$z = \frac{66 (- \frac{323}{274}) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{66 (- \frac{323}{274}) - 29}{31}$ .

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Step 6.2.1.1

Simplify the numerator.

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Step 6.2.1.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1.1

Move the leading negative in $- \frac{323}{274}$ into the numerator.

$z = \frac{66 (\frac{- 323}{274}) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.1.2

Factor $2$ out of $66$ .

$z = \frac{2 (33) (\frac{- 323}{274}) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.1.3

Factor $2$ out of $274$ .

$z = \frac{2 \cdot (33 (\frac{- 323}{2 \cdot 137})) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.1.4

Cancel the common factor.

$z = \frac{2 \cdot (33 (\frac{- 323}{2 \cdot 137})) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.1.5

Rewrite the expression.

$z = \frac{33 (\frac{- 323}{137}) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{33 (\frac{- 323}{137}) - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.2

Combine $33$ and $\frac{- 323}{137}$ .

$z = \frac{\frac{33 \cdot - 323}{137} - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.3

Multiply $33$ by $- 323$ .

$z = \frac{\frac{- 10659}{137} - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.4

Move the negative in front of the fraction.

$z = \frac{- \frac{10659}{137} - 29}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.5

To write $- 29$ as a fraction with a common denominator, multiply by $\frac{137}{137}$ .

$z = \frac{- \frac{10659}{137} - 29 \cdot \frac{137}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.6

Combine $- 29$ and $\frac{137}{137}$ .

$z = \frac{- \frac{10659}{137} + \frac{- 29 \cdot 137}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.7

Combine the numerators over the common denominator.

$z = \frac{\frac{- 10659 - 29 \cdot 137}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.8

Simplify the numerator.

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Step 6.2.1.1.8.1

Multiply $- 29$ by $137$ .

$z = \frac{\frac{- 10659 - 3973}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.8.2

Subtract $3973$ from $- 10659$ .

$z = \frac{\frac{- 14632}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{\frac{- 14632}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.1.9

Move the negative in front of the fraction.

$z = \frac{- \frac{14632}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{- \frac{14632}{137}}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$z = - \frac{14632}{137} \cdot \frac{1}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.3

Cancel the common factor of $31$ .

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Step 6.2.1.3.1

Move the leading negative in $- \frac{14632}{137}$ into the numerator.

$z = \frac{- 14632}{137} \cdot \frac{1}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.3.2

Factor $31$ out of $- 14632$ .

$z = \frac{31 (- 472)}{137} \cdot \frac{1}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.3.3

Cancel the common factor.

$z = \frac{31 \cdot - 472}{137} \cdot \frac{1}{31}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.3.4

Rewrite the expression.

$z = \frac{- 472}{137}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = \frac{- 472}{137}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.2.1.4

Move the negative in front of the fraction.

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{20 y}{31} - \frac{21}{31}$

Step 6.3

Replace all occurrences of $y$ in $x = \frac{20 y}{31} - \frac{21}{31}$ with $- \frac{323}{274}$ .

$x = \frac{20 (- \frac{323}{274})}{31} - \frac{21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{20 (- \frac{323}{274})}{31} - \frac{21}{31}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$x = \frac{20 (- \frac{323}{274}) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2

Simplify each term.

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Step 6.4.1.2.1

Cancel the common factor of $2$ .

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Step 6.4.1.2.1.1

Move the leading negative in $- \frac{323}{274}$ into the numerator.

$x = \frac{20 (\frac{- 323}{274}) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.1.2

Factor $2$ out of $20$ .

$x = \frac{2 (10) (\frac{- 323}{274}) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.1.3

Factor $2$ out of $274$ .

$x = \frac{2 \cdot (10 (\frac{- 323}{2 \cdot 137})) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.1.4

Cancel the common factor.

$x = \frac{2 \cdot (10 (\frac{- 323}{2 \cdot 137})) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.1.5

Rewrite the expression.

$x = \frac{10 (\frac{- 323}{137}) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{10 (\frac{- 323}{137}) - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.2

Combine $10$ and $\frac{- 323}{137}$ .

$x = \frac{\frac{10 \cdot - 323}{137} - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.3

Multiply $10$ by $- 323$ .

$x = \frac{\frac{- 3230}{137} - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.2.4

Move the negative in front of the fraction.

$x = \frac{- \frac{3230}{137} - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{- \frac{3230}{137} - 21}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.3

To write $- 21$ as a fraction with a common denominator, multiply by $\frac{137}{137}$ .

$x = \frac{- \frac{3230}{137} - 21 \cdot \frac{137}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.4

Combine $- 21$ and $\frac{137}{137}$ .

$x = \frac{- \frac{3230}{137} + \frac{- 21 \cdot 137}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.5

Combine the numerators over the common denominator.

$x = \frac{\frac{- 3230 - 21 \cdot 137}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.6

Simplify the numerator.

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Step 6.4.1.6.1

Multiply $- 21$ by $137$ .

$x = \frac{\frac{- 3230 - 2877}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.6.2

Subtract $2877$ from $- 3230$ .

$x = \frac{\frac{- 6107}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{\frac{- 6107}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.7

Move the negative in front of the fraction.

$x = \frac{- \frac{6107}{137}}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.8

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{6107}{137} \cdot \frac{1}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.9

Cancel the common factor of $31$ .

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Step 6.4.1.9.1

Move the leading negative in $- \frac{6107}{137}$ into the numerator.

$x = \frac{- 6107}{137} \cdot \frac{1}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.9.2

Factor $31$ out of $- 6107$ .

$x = \frac{31 (- 197)}{137} \cdot \frac{1}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.9.3

Cancel the common factor.

$x = \frac{31 \cdot - 197}{137} \cdot \frac{1}{31}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.9.4

Rewrite the expression.

$x = \frac{- 197}{137}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = \frac{- 197}{137}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 6.4.1.10

Move the negative in front of the fraction.

$x = - \frac{197}{137}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = - \frac{197}{137}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = - \frac{197}{137}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

$x = - \frac{197}{137}$

$z = - \frac{472}{137}$

$y = - \frac{323}{274}$

Step 7

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

$(- \frac{197}{137}, - \frac{323}{274}, - \frac{472}{137})$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- \frac{197}{137}, - \frac{323}{274}, - \frac{472}{137})$

Equation Form:

$x = - \frac{197}{137}, y = - \frac{323}{274}, z = - \frac{472}{137}$