Algebra Examples

$5 x + 2 y + z = 4$ $x + 2 z = 4$ $2 x + y - z = - 1$

Step 1

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

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Step 1.1

Subtract $5 x$ from both sides of the equation.

$2 y + z = 4 - 5 x$

$x + 2 z = 4$

$2 x + y - z = - 1$

Step 1.2

Subtract $2 y$ from both sides of the equation.

$z = 4 - 5 x - 2 y$

$x + 2 z = 4$

$2 x + y - z = - 1$

$z = 4 - 5 x - 2 y$

$x + 2 z = 4$

$2 x + y - z = - 1$

Step 2

Replace all occurrences of $z$ with $4 - 5 x - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $z$ in $x + 2 z = 4$ with $4 - 5 x - 2 y$ .

$x + 2 (4 - 5 x - 2 y) = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x + 2 (4 - 5 x - 2 y)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$x + 2 \cdot 4 + 2 (- 5 x) + 2 (- 2 y) = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $2$ by $4$ .

$x + 8 + 2 (- 5 x) + 2 (- 2 y) = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

Step 2.2.1.1.2.2

Multiply $- 5$ by $2$ .

$x + 8 - 10 x + 2 (- 2 y) = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

Step 2.2.1.1.2.3

Multiply $- 2$ by $2$ .

$x + 8 - 10 x - 4 y = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

$x + 8 - 10 x - 4 y = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

$x + 8 - 10 x - 4 y = 4$

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

Step 2.2.1.2

Subtract $10 x$ from $x$ .

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

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

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

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

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

$z = 4 - 5 x - 2 y$

$2 x + y - z = - 1$

Step 2.3

Replace all occurrences of $z$ in $2 x + y - z = - 1$ with $4 - 5 x - 2 y$ .

$2 x + y - (4 - 5 x - 2 y) = - 1$

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

$z = 4 - 5 x - 2 y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $2 x + y - (4 - 5 x - 2 y)$ .

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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.

$2 x + y - 1 \cdot 4 - (- 5 x) - (- 2 y) = - 1$

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

$z = 4 - 5 x - 2 y$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $- 1$ by $4$ .

$2 x + y - 4 - (- 5 x) - (- 2 y) = - 1$

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

$z = 4 - 5 x - 2 y$

Step 2.4.1.1.2.2

Multiply $- 5$ by $- 1$ .

$2 x + y - 4 + 5 x - (- 2 y) = - 1$

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

$z = 4 - 5 x - 2 y$

Step 2.4.1.1.2.3

Multiply $- 2$ by $- 1$ .

$2 x + y - 4 + 5 x + 2 y = - 1$

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

$z = 4 - 5 x - 2 y$

$2 x + y - 4 + 5 x + 2 y = - 1$

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

$z = 4 - 5 x - 2 y$

$2 x + y - 4 + 5 x + 2 y = - 1$

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

$z = 4 - 5 x - 2 y$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $2 x$ and $5 x$ .

$7 x + y - 4 + 2 y = - 1$

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

$z = 4 - 5 x - 2 y$

Step 2.4.1.2.2

Add $y$ and $2 y$ .

$7 x + 3 y - 4 = - 1$

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

$z = 4 - 5 x - 2 y$

$7 x + 3 y - 4 = - 1$

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

$z = 4 - 5 x - 2 y$

$7 x + 3 y - 4 = - 1$

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

$z = 4 - 5 x - 2 y$

$7 x + 3 y - 4 = - 1$

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

$z = 4 - 5 x - 2 y$

$7 x + 3 y - 4 = - 1$

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

$z = 4 - 5 x - 2 y$

Step 3

Solve for $x$ in $7 x + 3 y - 4 = - 1$ .

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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

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

$7 x - 4 = - 1 - 3 y$

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

$z = 4 - 5 x - 2 y$

Step 3.1.2

Add $4$ to both sides of the equation.

$7 x = - 1 - 3 y + 4$

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

$z = 4 - 5 x - 2 y$

Step 3.1.3

Add $- 1$ and $4$ .

$7 x = - 3 y + 3$

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

$z = 4 - 5 x - 2 y$

$7 x = - 3 y + 3$

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

$z = 4 - 5 x - 2 y$

Step 3.2

Divide each term in $7 x = - 3 y + 3$ by $7$ and simplify.

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Step 3.2.1

Divide each term in $7 x = - 3 y + 3$ by $7$ .

$\frac{7 x}{7} = \frac{- 3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $7$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

$x = \frac{- 3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

$x = \frac{- 3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

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.

$x = - \frac{3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

$x = - \frac{3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

$x = - \frac{3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

$x = - \frac{3 y}{7} + \frac{3}{7}$

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

$z = 4 - 5 x - 2 y$

Step 4

Replace all occurrences of $x$ with $- \frac{3 y}{7} + \frac{3}{7}$ in each equation.

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Step 4.1

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

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

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- 9 (- \frac{3 y}{7} + \frac{3}{7}) + 8 - 4 y$ .

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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.

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

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.1.2

Multiply $- 9 (- \frac{3 y}{7})$ .

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Step 4.2.1.1.2.1

Multiply $- 1$ by $- 9$ .

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

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.1.2.2

Combine $9$ and $\frac{3 y}{7}$ .

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

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.1.2.3

Multiply $3$ by $9$ .

$\frac{27 y}{7} - 9 (\frac{3}{7}) + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$\frac{27 y}{7} - 9 (\frac{3}{7}) + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.1.3

Multiply $- 9 (\frac{3}{7})$ .

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Step 4.2.1.1.3.1

Combine $- 9$ and $\frac{3}{7}$ .

$\frac{27 y}{7} + \frac{- 9 \cdot 3}{7} + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.1.3.2

Multiply $- 9$ by $3$ .

$\frac{27 y}{7} + \frac{- 27}{7} + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$\frac{27 y}{7} + \frac{- 27}{7} + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.1.4

Move the negative in front of the fraction.

$\frac{27 y}{7} - \frac{27}{7} + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$\frac{27 y}{7} - \frac{27}{7} + 8 - 4 y = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.2

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{27 y}{7} - 4 y \cdot \frac{7}{7} - \frac{27}{7} + 8 = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.3

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

$\frac{27 y}{7} + \frac{- 4 y \cdot 7}{7} - \frac{27}{7} + 8 = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{27 y - 4 y \cdot 7}{7} - \frac{27}{7} + 8 = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.5

Combine the numerators over the common denominator.

$8 + \frac{27 y - 4 y \cdot 7 - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.6

Multiply $7$ by $- 4$ .

$8 + \frac{27 y - 28 y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.7

Subtract $28 y$ from $27 y$ .

$8 + \frac{- y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.8

To write $8$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$8 \cdot \frac{7}{7} + \frac{- y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.9

Simplify terms.

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Step 4.2.1.9.1

Combine $8$ and $\frac{7}{7}$ .

$\frac{8 \cdot 7}{7} + \frac{- y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.9.2

Combine the numerators over the common denominator.

$\frac{8 \cdot 7 - y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$\frac{8 \cdot 7 - y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.10

Simplify the numerator.

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Step 4.2.1.10.1

Multiply $8$ by $7$ .

$\frac{56 - y - 27}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.10.2

Subtract $27$ from $56$ .

$\frac{- y + 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$\frac{- y + 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.11

Simplify with factoring out.

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Step 4.2.1.11.1

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

$\frac{- (y) + 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.11.2

Rewrite $29$ as $- 1 (- 29)$ .

$\frac{- (y) - 1 \cdot - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.11.3

Factor $- 1$ out of $- (y) - 1 (- 29)$ .

$\frac{- (y - 29)}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.11.4

Simplify the expression.

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Step 4.2.1.11.4.1

Rewrite $- (y - 29)$ as $- 1 (y - 29)$ .

$\frac{- 1 (y - 29)}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.2.1.11.4.2

Move the negative in front of the fraction.

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 - 5 x - 2 y$

Step 4.3

Replace all occurrences of $x$ in $z = 4 - 5 x - 2 y$ with $- \frac{3 y}{7} + \frac{3}{7}$ .

$z = 4 - 5 (- \frac{3 y}{7} + \frac{3}{7}) - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $4 - 5 (- \frac{3 y}{7} + \frac{3}{7}) - 2 y$ .

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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.

$z = 4 - 5 (- \frac{3 y}{7}) - 5 (\frac{3}{7}) - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.1.2

Multiply $- 5 (- \frac{3 y}{7})$ .

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Step 4.4.1.1.2.1

Multiply $- 1$ by $- 5$ .

$z = 4 + 5 (\frac{3 y}{7}) - 5 (\frac{3}{7}) - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.1.2.2

Combine $5$ and $\frac{3 y}{7}$ .

$z = 4 + \frac{5 (3 y)}{7} - 5 (\frac{3}{7}) - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.1.2.3

Multiply $3$ by $5$ .

$z = 4 + \frac{15 y}{7} - 5 (\frac{3}{7}) - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 + \frac{15 y}{7} - 5 (\frac{3}{7}) - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.1.3

Multiply $- 5 (\frac{3}{7})$ .

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Step 4.4.1.1.3.1

Combine $- 5$ and $\frac{3}{7}$ .

$z = 4 + \frac{15 y}{7} + \frac{- 5 \cdot 3}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.1.3.2

Multiply $- 5$ by $3$ .

$z = 4 + \frac{15 y}{7} + \frac{- 15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 + \frac{15 y}{7} + \frac{- 15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$z = 4 + \frac{15 y}{7} - \frac{15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 4 + \frac{15 y}{7} - \frac{15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$z = \frac{15 y}{7} + 4 \cdot \frac{7}{7} - \frac{15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.3

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

$z = \frac{15 y}{7} + \frac{4 \cdot 7}{7} - \frac{15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$z = \frac{15 y}{7} + \frac{4 \cdot 7 - 15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $4$ by $7$ .

$z = \frac{15 y}{7} + \frac{28 - 15}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.5.2

Subtract $15$ from $28$ .

$z = \frac{15 y}{7} + \frac{13}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = \frac{15 y}{7} + \frac{13}{7} - 2 y$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.6

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$z = \frac{15 y}{7} - 2 y \cdot \frac{7}{7} + \frac{13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.7

Combine $- 2 y$ and $\frac{7}{7}$ .

$z = \frac{15 y}{7} + \frac{- 2 y \cdot 7}{7} + \frac{13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.8

Combine the numerators over the common denominator.

$z = \frac{15 y - 2 y \cdot 7}{7} + \frac{13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$z = \frac{15 y - 2 y \cdot 7 + 13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.10

Multiply $7$ by $- 2$ .

$z = \frac{15 y - 14 y + 13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 4.4.1.11

Subtract $14 y$ from $15 y$ .

$z = \frac{y + 13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = \frac{y + 13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = \frac{y + 13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = \frac{y + 13}{7}$

$- \frac{y - 29}{7} = 4$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5

Solve for $y$ in $- \frac{y - 29}{7} = 4$ .

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Step 5.1

Multiply both sides of the equation by $- 7$ .

$- 7 (- \frac{y - 29}{7}) = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

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 $- 7 (- \frac{y - 29}{7})$ .

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Step 5.2.1.1.1

Cancel the common factor of $7$ .

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Step 5.2.1.1.1.1

Move the leading negative in $- \frac{y - 29}{7}$ into the numerator.

$- 7 \frac{- (y - 29)}{7} = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.2.1.1.1.2

Factor $7$ out of $- 7$ .

$7 (- 1) (\frac{- (y - 29)}{7}) = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.2.1.1.1.3

Cancel the common factor.

$7 \cdot (- 1 \frac{- (y - 29)}{7}) = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.2.1.1.1.4

Rewrite the expression.

$y - 29 = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y - 29 = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.2.1.1.2

Multiply.

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Step 5.2.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (y - 29) = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.2.1.1.2.2

Multiply $y - 29$ by $1$ .

$y - 29 = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y - 29 = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y - 29 = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y - 29 = - 7 \cdot 4$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Multiply $- 7$ by $4$ .

$y - 29 = - 28$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y - 29 = - 28$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y - 29 = - 28$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.3

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

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Step 5.3.1

Add $29$ to both sides of the equation.

$y = - 28 + 29$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 5.3.2

Add $- 28$ and $29$ .

$y = 1$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y = 1$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$y = 1$

$z = \frac{y + 13}{7}$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 6

Replace all occurrences of $y$ with $1$ in each equation.

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Step 6.1

Replace all occurrences of $y$ in $z = \frac{y + 13}{7}$ with $1$ .

$z = \frac{(1) + 13}{7}$

$y = 1$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{(1) + 13}{7}$ .

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Step 6.2.1.1

Add $1$ and $13$ .

$z = \frac{14}{7}$

$y = 1$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 6.2.1.2

Divide $14$ by $7$ .

$z = 2$

$y = 1$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 2$

$y = 1$

$x = - \frac{3 y}{7} + \frac{3}{7}$

$z = 2$

$y = 1$

$x = - \frac{3 y}{7} + \frac{3}{7}$

Step 6.3

Replace all occurrences of $y$ in $x = - \frac{3 y}{7} + \frac{3}{7}$ with $1$ .

$x = - \frac{3 (1)}{7} + \frac{3}{7}$

$z = 2$

$y = 1$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $- \frac{3 (1)}{7} + \frac{3}{7}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

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

$z = 2$

$y = 1$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $- 3$ by $1$ .

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

$z = 2$

$y = 1$

Step 6.4.1.2.2

Add $- 3$ and $3$ .

$x = \frac{0}{7}$

$z = 2$

$y = 1$

Step 6.4.1.2.3

Divide $0$ by $7$ .

$x = 0$

$z = 2$

$y = 1$

$x = 0$

$z = 2$

$y = 1$

$x = 0$

$z = 2$

$y = 1$

$x = 0$

$z = 2$

$y = 1$

$x = 0$

$z = 2$

$y = 1$

Step 7

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

$(0, 1, 2)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(0, 1, 2)$

Equation Form:

$x = 0, y = 1, z = 2$