Algebra Examples

$- x + 3 y + z = 3$ , $x - y + 2 z = 0$ , $3 x - 5 y + 2 z = - 2$

Step 1

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

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Step 1.1

Add $x$ to both sides of the equation.

$3 y + z = 3 + x$

$x - y + 2 z = 0$

$3 x - 5 y + 2 z = - 2$

Step 1.2

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

$z = 3 + x - 3 y$

$x - y + 2 z = 0$

$3 x - 5 y + 2 z = - 2$

$z = 3 + x - 3 y$

$x - y + 2 z = 0$

$3 x - 5 y + 2 z = - 2$

Step 2

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

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Step 2.1

Replace all occurrences of $z$ in $x - y + 2 z = 0$ with $3 + x - 3 y$ .

$x - y + 2 (3 + x - 3 y) = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$x - y + 2 \cdot 3 + 2 x + 2 (- 3 y) = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $2$ by $3$ .

$x - y + 6 + 2 x + 2 (- 3 y) = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

Step 2.2.1.1.2.2

Multiply $- 3$ by $2$ .

$x - y + 6 + 2 x - 6 y = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

$x - y + 6 + 2 x - 6 y = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

$x - y + 6 + 2 x - 6 y = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $x$ and $2 x$ .

$3 x - y + 6 - 6 y = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

Step 2.2.1.2.2

Subtract $6 y$ from $- y$ .

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 2 z = - 2$

Step 2.3

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

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

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 2.4

Simplify the left side.

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Step 2.4.1

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

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

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

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $2$ by $3$ .

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

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 2.4.1.1.2.2

Multiply $- 3$ by $2$ .

$3 x - 5 y + 6 + 2 x - 6 y = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 6 + 2 x - 6 y = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$3 x - 5 y + 6 + 2 x - 6 y = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $3 x$ and $2 x$ .

$5 x - 5 y + 6 - 6 y = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 2.4.1.2.2

Subtract $6 y$ from $- 5 y$ .

$5 x - 11 y + 6 = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$5 x - 11 y + 6 = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$5 x - 11 y + 6 = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$5 x - 11 y + 6 = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$5 x - 11 y + 6 = - 2$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3

Solve for $x$ in $5 x - 11 y + 6 = - 2$ .

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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 $11 y$ to both sides of the equation.

$5 x + 6 = - 2 + 11 y$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3.1.2

Subtract $6$ from both sides of the equation.

$5 x = - 2 + 11 y - 6$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3.1.3

Subtract $6$ from $- 2$ .

$5 x = 11 y - 8$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$5 x = 11 y - 8$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3.2

Divide each term in $5 x = 11 y - 8$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 x = 11 y - 8$ by $5$ .

$\frac{5 x}{5} = \frac{11 y}{5} + \frac{- 8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{11 y}{5} + \frac{- 8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{11 y}{5} + \frac{- 8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$x = \frac{11 y}{5} + \frac{- 8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$x = \frac{11 y}{5} + \frac{- 8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = \frac{11 y}{5} - \frac{8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$x = \frac{11 y}{5} - \frac{8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$x = \frac{11 y}{5} - \frac{8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

$x = \frac{11 y}{5} - \frac{8}{5}$

$3 x - 7 y + 6 = 0$

$z = 3 + x - 3 y$

Step 4

Replace all occurrences of $x$ with $\frac{11 y}{5} - \frac{8}{5}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $3 x - 7 y + 6 = 0$ with $\frac{11 y}{5} - \frac{8}{5}$ .

$3 (\frac{11 y}{5} - \frac{8}{5}) - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $3 (\frac{11 y}{5} - \frac{8}{5}) - 7 y + 6$ .

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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.

$3 (\frac{11 y}{5}) + 3 (- \frac{8}{5}) - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.1.2

Multiply $3 \frac{11 y}{5}$ .

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Step 4.2.1.1.2.1

Combine $3$ and $\frac{11 y}{5}$ .

$\frac{3 (11 y)}{5} + 3 (- \frac{8}{5}) - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.1.2.2

Multiply $11$ by $3$ .

$\frac{33 y}{5} + 3 (- \frac{8}{5}) - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$\frac{33 y}{5} + 3 (- \frac{8}{5}) - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.1.3

Multiply $3 (- \frac{8}{5})$ .

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Step 4.2.1.1.3.1

Multiply $- 1$ by $3$ .

$\frac{33 y}{5} - 3 (\frac{8}{5}) - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.1.3.2

Combine $- 3$ and $\frac{8}{5}$ .

$\frac{33 y}{5} + \frac{- 3 \cdot 8}{5} - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.1.3.3

Multiply $- 3$ by $8$ .

$\frac{33 y}{5} + \frac{- 24}{5} - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$\frac{33 y}{5} + \frac{- 24}{5} - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.1.4

Move the negative in front of the fraction.

$\frac{33 y}{5} - \frac{24}{5} - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$\frac{33 y}{5} - \frac{24}{5} - 7 y + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.2

To write $- 7 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{33 y}{5} - 7 y \cdot \frac{5}{5} - \frac{24}{5} + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.3

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

$\frac{33 y}{5} + \frac{- 7 y \cdot 5}{5} - \frac{24}{5} + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{33 y - 7 y \cdot 5}{5} - \frac{24}{5} + 6 = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.5

Combine the numerators over the common denominator.

$6 + \frac{33 y - 7 y \cdot 5 - 24}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.6

Multiply $5$ by $- 7$ .

$6 + \frac{33 y - 35 y - 24}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.7

Subtract $35 y$ from $33 y$ .

$6 + \frac{- 2 y - 24}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.8

Factor $2$ out of $- 2 y - 24$ .

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Step 4.2.1.8.1

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

$6 + \frac{2 (- y) - 24}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.8.2

Factor $2$ out of $- 24$ .

$6 + \frac{2 (- y) + 2 (- 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.8.3

Factor $2$ out of $2 (- y) + 2 (- 12)$ .

$6 + \frac{2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$6 + \frac{2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.9

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$6 \cdot \frac{5}{5} + \frac{2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.10

Simplify terms.

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Step 4.2.1.10.1

Combine $6$ and $\frac{5}{5}$ .

$\frac{6 \cdot 5}{5} + \frac{2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.10.2

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 + 2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$\frac{6 \cdot 5 + 2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.11

Simplify the numerator.

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Step 4.2.1.11.1

Factor $2$ out of $6 \cdot 5 + 2 (- y - 12)$ .

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Step 4.2.1.11.1.1

Factor $2$ out of $6 \cdot 5$ .

$\frac{2 (3 \cdot 5) + 2 (- y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.11.1.2

Factor $2$ out of $2 (3 \cdot 5) + 2 (- y - 12)$ .

$\frac{2 (3 \cdot 5 - y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$\frac{2 (3 \cdot 5 - y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.11.2

Multiply $3$ by $5$ .

$\frac{2 (15 - y - 12)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.11.3

Subtract $12$ from $15$ .

$\frac{2 (- y + 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$\frac{2 (- y + 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.12

Simplify with factoring out.

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Step 4.2.1.12.1

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

$\frac{2 (- (y) + 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.12.2

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

$\frac{2 (- (y) - 1 \cdot - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.12.3

Factor $- 1$ out of $- (y) - 1 (- 3)$ .

$\frac{2 (- (y - 3))}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.12.4

Simplify the expression.

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Step 4.2.1.12.4.1

Rewrite $- (y - 3)$ as $- 1 (y - 3)$ .

$\frac{2 (- 1 (y - 3))}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.2.1.12.4.2

Move the negative in front of the fraction.

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + x - 3 y$

Step 4.3

Replace all occurrences of $x$ in $z = 3 + x - 3 y$ with $\frac{11 y}{5} - \frac{8}{5}$ .

$z = 3 + \frac{11 y}{5} - \frac{8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4

Simplify $z = 3 + \frac{11 y}{5} - \frac{8}{5} - 3 y$ .

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Step 4.4.1

Simplify the left side.

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Step 4.4.1.1

Remove parentheses.

$z = 3 + \frac{11 y}{5} - \frac{8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = 3 + \frac{11 y}{5} - \frac{8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2

Simplify the right side.

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Step 4.4.2.1

Simplify $3 + \frac{11 y}{5} - \frac{8}{5} - 3 y$ .

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Step 4.4.2.1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$z = \frac{11 y}{5} + 3 \cdot \frac{5}{5} - \frac{8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.2

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

$z = \frac{11 y}{5} + \frac{3 \cdot 5}{5} - \frac{8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.3

Combine the numerators over the common denominator.

$z = \frac{11 y}{5} + \frac{3 \cdot 5 - 8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.4

Simplify the numerator.

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Step 4.4.2.1.4.1

Multiply $3$ by $5$ .

$z = \frac{11 y}{5} + \frac{15 - 8}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.4.2

Subtract $8$ from $15$ .

$z = \frac{11 y}{5} + \frac{7}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = \frac{11 y}{5} + \frac{7}{5} - 3 y$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.5

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$z = \frac{11 y}{5} - 3 y \cdot \frac{5}{5} + \frac{7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.6

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

$z = \frac{11 y}{5} + \frac{- 3 y \cdot 5}{5} + \frac{7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.7

Combine the numerators over the common denominator.

$z = \frac{11 y - 3 y \cdot 5}{5} + \frac{7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.8

Combine the numerators over the common denominator.

$z = \frac{11 y - 3 y \cdot 5 + 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.9

Multiply $5$ by $- 3$ .

$z = \frac{11 y - 15 y + 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.10

Subtract $15 y$ from $11 y$ .

$z = \frac{- 4 y + 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.11

Factor $- 1$ out of $- 4 y$ .

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

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.12

Rewrite $7$ as $- 1 (- 7)$ .

$z = \frac{- (4 y) - 1 \cdot - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.13

Factor $- 1$ out of $- (4 y) - 1 (- 7)$ .

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

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.14

Simplify the expression.

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Step 4.4.2.1.14.1

Rewrite $- (4 y - 7)$ as $- 1 (4 y - 7)$ .

$z = \frac{- 1 (4 y - 7)}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 4.4.2.1.14.2

Move the negative in front of the fraction.

$z = - \frac{4 y - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - \frac{4 y - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - \frac{4 y - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - \frac{4 y - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - \frac{4 y - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - \frac{4 y - 7}{5}$

$- \frac{2 (y - 3)}{5} = 0$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 5

Solve for $y$ in $- \frac{2 (y - 3)}{5} = 0$ .

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Step 5.1

Set the numerator equal to zero.

$2 (y - 3) = 0$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 5.2

Solve the equation for $y$ .

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Step 5.2.1

Divide each term in $2 (y - 3) = 0$ by $2$ and simplify.

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Step 5.2.1.1

Divide each term in $2 (y - 3) = 0$ by $2$ .

$\frac{2 (y - 3)}{2} = \frac{0}{2}$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 5.2.1.2

Simplify the left side.

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Step 5.2.1.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.2.1.1

Cancel the common factor.

$\frac{2 (y - 3)}{2} = \frac{0}{2}$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 5.2.1.2.1.2

Divide $y - 3$ by $1$ .

$y - 3 = \frac{0}{2}$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

$y - 3 = \frac{0}{2}$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

$y - 3 = \frac{0}{2}$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 5.2.1.3

Simplify the right side.

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Step 5.2.1.3.1

Divide $0$ by $2$ .

$y - 3 = 0$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

$y - 3 = 0$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

$y - 3 = 0$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 5.2.2

Add $3$ to both sides of the equation.

$y = 3$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

$y = 3$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

$y = 3$

$z = - \frac{4 y - 7}{5}$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6

Replace all occurrences of $y$ with $3$ in each equation.

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Step 6.1

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

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

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6.2

Simplify the right side.

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Step 6.2.1

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

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Step 6.2.1.1

Simplify the numerator.

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Step 6.2.1.1.1

Multiply $4$ by $3$ .

$z = - \frac{12 - 7}{5}$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6.2.1.1.2

Subtract $7$ from $12$ .

$z = - \frac{5}{5}$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - \frac{5}{5}$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6.2.1.2

Reduce the expression by cancelling the common factors.

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Step 6.2.1.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.2.1.1

Cancel the common factor.

$z = - \frac{5}{5}$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6.2.1.2.1.2

Rewrite the expression.

$z = - 1 \cdot 1$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - 1 \cdot 1$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6.2.1.2.2

Multiply $- 1$ by $1$ .

$z = - 1$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - 1$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - 1$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

$z = - 1$

$y = 3$

$x = \frac{11 y}{5} - \frac{8}{5}$

Step 6.3

Replace all occurrences of $y$ in $x = \frac{11 y}{5} - \frac{8}{5}$ with $3$ .

$x = \frac{11 (3)}{5} - \frac{8}{5}$

$z = - 1$

$y = 3$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{11 (3)}{5} - \frac{8}{5}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$x = \frac{11 (3) - 8}{5}$

$z = - 1$

$y = 3$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $11$ by $3$ .

$x = \frac{33 - 8}{5}$

$z = - 1$

$y = 3$

Step 6.4.1.2.2

Subtract $8$ from $33$ .

$x = \frac{25}{5}$

$z = - 1$

$y = 3$

Step 6.4.1.2.3

Divide $25$ by $5$ .

$x = 5$

$z = - 1$

$y = 3$

$x = 5$

$z = - 1$

$y = 3$

$x = 5$

$z = - 1$

$y = 3$

$x = 5$

$z = - 1$

$y = 3$

$x = 5$

$z = - 1$

$y = 3$

Step 7

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

$(5, 3, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(5, 3, - 1)$

Equation Form:

$x = 5, y = 3, z = - 1$