Algebra Examples

$2 x + 4 y + z = 1$ $x - 2 y - 3 z = 2$ $x + y - z = - 1$

Step 1

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

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Step 1.1

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

$4 y + z = 1 - 2 x$

$x - 2 y - 3 z = 2$

$x + y - z = - 1$

Step 1.2

Subtract $4 y$ from both sides of the equation.

$z = 1 - 2 x - 4 y$

$x - 2 y - 3 z = 2$

$x + y - z = - 1$

$z = 1 - 2 x - 4 y$

$x - 2 y - 3 z = 2$

$x + y - z = - 1$

Step 2

Replace all occurrences of $z$ with $1 - 2 x - 4 y$ in each equation.

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Step 2.1

Replace all occurrences of $z$ in $x - 2 y - 3 z = 2$ with $1 - 2 x - 4 y$ .

$x - 2 y - 3 (1 - 2 x - 4 y) = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x - 2 y - 3 (1 - 2 x - 4 y)$ .

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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.

$x - 2 y - 3 \cdot 1 - 3 (- 2 x) - 3 (- 4 y) = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $- 3$ by $1$ .

$x - 2 y - 3 - 3 (- 2 x) - 3 (- 4 y) = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.2.1.1.2.2

Multiply $- 2$ by $- 3$ .

$x - 2 y - 3 + 6 x - 3 (- 4 y) = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.2.1.1.2.3

Multiply $- 4$ by $- 3$ .

$x - 2 y - 3 + 6 x + 12 y = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

$x - 2 y - 3 + 6 x + 12 y = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

$x - 2 y - 3 + 6 x + 12 y = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $x$ and $6 x$ .

$7 x - 2 y - 3 + 12 y = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.2.1.2.2

Add $- 2 y$ and $12 y$ .

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x + y - z = - 1$

Step 2.3

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

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $x + y - (1 - 2 x - 4 y)$ .

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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.

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $- 1$ by $1$ .

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 2.4.1.1.2.2

Multiply $- 2$ by $- 1$ .

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 2.4.1.1.2.3

Multiply $- 4$ by $- 1$ .

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $x$ and $2 x$ .

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 2.4.1.2.2

Add $y$ and $4 y$ .

$3 x + 5 y - 1 = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$3 x + 5 y - 1 = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$3 x + 5 y - 1 = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$3 x + 5 y - 1 = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$3 x + 5 y - 1 = - 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3

Solve for $x$ in $3 x + 5 y - 1 = - 1$ .

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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 $5 y$ from both sides of the equation.

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

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3.1.2

Add $1$ to both sides of the equation.

$3 x = - 1 - 5 y + 1$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3.1.3

Combine the opposite terms in $- 1 - 5 y + 1$ .

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Step 3.1.3.1

Add $- 1$ and $1$ .

$3 x = - 5 y + 0$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3.1.3.2

Add $- 5 y$ and $0$ .

$3 x = - 5 y$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$3 x = - 5 y$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$3 x = - 5 y$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3.2

Divide each term in $3 x = - 5 y$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = - 5 y$ by $3$ .

$\frac{3 x}{3} = \frac{- 5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x = \frac{- 5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x = \frac{- 5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

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.

$x = - \frac{5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x = - \frac{5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x = - \frac{5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

$x = - \frac{5 y}{3}$

$7 x + 10 y - 3 = 2$

$z = 1 - 2 x - 4 y$

Step 4

Replace all occurrences of $x$ with $- \frac{5 y}{3}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $7 x + 10 y - 3 = 2$ with $- \frac{5 y}{3}$ .

$7 (- \frac{5 y}{3}) + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $7 (- \frac{5 y}{3}) + 10 y - 3$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

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

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Step 4.2.1.1.1.1

Multiply $- 1$ by $7$ .

$- 7 \frac{5 y}{3} + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.1.1.2

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

$\frac{- 7 (5 y)}{3} + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.1.1.3

Multiply $5$ by $- 7$ .

$\frac{- 35 y}{3} + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$\frac{- 35 y}{3} + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.1.2

Move the negative in front of the fraction.

$- \frac{35 y}{3} + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$- \frac{35 y}{3} + 10 y - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.2

To write $10 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{35 y}{3} + 10 y \cdot \frac{3}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.3

Simplify terms.

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Step 4.2.1.3.1

Combine $10 y$ and $\frac{3}{3}$ .

$- \frac{35 y}{3} + \frac{10 y \cdot 3}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.3.2

Combine the numerators over the common denominator.

$\frac{- 35 y + 10 y \cdot 3}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$\frac{- 35 y + 10 y \cdot 3}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4

Simplify each term.

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Step 4.2.1.4.1

Simplify the numerator.

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Step 4.2.1.4.1.1

Factor $5 y$ out of $- 35 y + 10 y \cdot 3$ .

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Step 4.2.1.4.1.1.1

Factor $5 y$ out of $- 35 y$ .

$\frac{5 y (- 7) + 10 y \cdot 3}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4.1.1.2

Factor $5 y$ out of $10 y \cdot 3$ .

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

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4.1.1.3

Factor $5 y$ out of $5 y (- 7) + 5 y (2 \cdot 3)$ .

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

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

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

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4.1.2

Multiply $2$ by $3$ .

$\frac{5 y (- 7 + 6)}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4.1.3

Add $- 7$ and $6$ .

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

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4.1.4

Multiply $- 1$ by $5$ .

$\frac{- 5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$\frac{- 5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.2.1.4.2

Move the negative in front of the fraction.

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - 2 x - 4 y$

Step 4.3

Replace all occurrences of $x$ in $z = 1 - 2 x - 4 y$ with $- \frac{5 y}{3}$ .

$z = 1 - 2 (- \frac{5 y}{3}) - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $1 - 2 (- \frac{5 y}{3}) - 4 y$ .

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Step 4.4.1.1

Multiply $- 2 (- \frac{5 y}{3})$ .

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Step 4.4.1.1.1

Multiply $- 1$ by $- 2$ .

$z = 1 + 2 (\frac{5 y}{3}) - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.1.2

Combine $2$ and $\frac{5 y}{3}$ .

$z = 1 + \frac{2 (5 y)}{3} - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.1.3

Multiply $5$ by $2$ .

$z = 1 + \frac{10 y}{3} - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 + \frac{10 y}{3} - 4 y$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.2

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z = 1 + \frac{10 y}{3} - 4 y \cdot \frac{3}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.3

Simplify terms.

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Step 4.4.1.3.1

Combine $- 4 y$ and $\frac{3}{3}$ .

$z = 1 + \frac{10 y}{3} + \frac{- 4 y \cdot 3}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.3.2

Combine the numerators over the common denominator.

$z = 1 + \frac{10 y - 4 y \cdot 3}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 + \frac{10 y - 4 y \cdot 3}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4

Simplify each term.

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Step 4.4.1.4.1

Simplify the numerator.

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Step 4.4.1.4.1.1

Factor $2 y$ out of $10 y - 4 y \cdot 3$ .

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Step 4.4.1.4.1.1.1

Factor $2 y$ out of $10 y$ .

$z = 1 + \frac{2 y (5) - 4 y \cdot 3}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4.1.1.2

Factor $2 y$ out of $- 4 y \cdot 3$ .

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

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4.1.1.3

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

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

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

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

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4.1.2

Multiply $- 2$ by $3$ .

$z = 1 + \frac{2 y (5 - 6)}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4.1.3

Subtract $6$ from $5$ .

$z = 1 + \frac{2 y \cdot - 1}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4.1.4

Multiply $- 1$ by $2$ .

$z = 1 + \frac{- 2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 + \frac{- 2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 4.4.1.4.2

Move the negative in front of the fraction.

$z = 1 - \frac{2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - \frac{2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - \frac{2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - \frac{2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

$z = 1 - \frac{2 y}{3}$

$- \frac{5 y}{3} - 3 = 2$

$x = - \frac{5 y}{3}$

Step 5

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

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Step 5.1

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

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Step 5.1.1

Add $3$ to both sides of the equation.

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.1.2

Add $2$ and $3$ .

$- \frac{5 y}{3} = 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$- \frac{5 y}{3} = 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.2

Multiply both sides of the equation by $- \frac{3}{5}$ .

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3

Simplify both sides of the equation.

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Step 5.3.1

Simplify the left side.

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Step 5.3.1.1

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

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Step 5.3.1.1.1

Cancel the common factor of $3$ .

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Step 5.3.1.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.1.2

Move the leading negative in $- \frac{5 y}{3}$ into the numerator.

$\frac{- 3}{5} \cdot \frac{- 5 y}{3} = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.1.3

Factor $3$ out of $- 3$ .

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{5} \cdot \frac{- 5 y}{3} = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.1.5

Rewrite the expression.

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.2

Cancel the common factor of $5$ .

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Step 5.3.1.1.2.1

Factor $5$ out of $- 5 y$ .

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.2.2

Cancel the common factor.

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

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.2.3

Rewrite the expression.

$y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.3

Multiply.

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Step 5.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - \frac{3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.2

Simplify the right side.

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Step 5.3.2.1

Cancel the common factor of $5$ .

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Step 5.3.2.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$y = \frac{- 3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.2.1.2

Cancel the common factor.

$y = \frac{- 3}{5} \cdot 5$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

Step 5.3.2.1.3

Rewrite the expression.

$y = - 3$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - 3$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - 3$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - 3$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

$y = - 3$

$z = 1 - \frac{2 y}{3}$

$x = - \frac{5 y}{3}$

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 $z = 1 - \frac{2 y}{3}$ with $- 3$ .

$z = 1 - \frac{2 (- 3)}{3}$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $1 - \frac{2 (- 3)}{3}$ .

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Step 6.2.1.1

Simplify each term.

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Step 6.2.1.1.1

Cancel the common factor of $- 3$ and $3$ .

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Step 6.2.1.1.1.1

Factor $3$ out of $2 (- 3)$ .

$z = 1 - \frac{3 (2 \cdot (- 1))}{3}$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.1.1.2

Cancel the common factors.

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Step 6.2.1.1.1.2.1

Factor $3$ out of $3$ .

$z = 1 - \frac{3 (2 \cdot (- 1))}{3 (1)}$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.1.1.2.2

Cancel the common factor.

$z = 1 - \frac{3 (2 \cdot (- 1))}{3 \cdot 1}$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.1.1.2.3

Rewrite the expression.

$z = 1 - \frac{2 \cdot (- 1)}{1}$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.1.1.2.4

Divide $2 \cdot (- 1)$ by $1$ .

$z = 1 - (2 \cdot (- 1))$

$y = - 3$

$x = - \frac{5 y}{3}$

$z = 1 - (2 \cdot (- 1))$

$y = - 3$

$x = - \frac{5 y}{3}$

$z = 1 - (2 \cdot (- 1))$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.1.2

Multiply $- (2 \cdot (- 1))$ .

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Step 6.2.1.1.2.1

Multiply $2$ by $- 1$ .

$z = 1 + 2$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.1.2.2

Multiply $- 1$ by $- 2$ .

$z = 1 + 2$

$y = - 3$

$x = - \frac{5 y}{3}$

$z = 1 + 2$

$y = - 3$

$x = - \frac{5 y}{3}$

$z = 1 + 2$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.2.1.2

Add $1$ and $2$ .

$z = 3$

$y = - 3$

$x = - \frac{5 y}{3}$

$z = 3$

$y = - 3$

$x = - \frac{5 y}{3}$

$z = 3$

$y = - 3$

$x = - \frac{5 y}{3}$

Step 6.3

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

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

$z = 3$

$y = - 3$

Step 6.4

Simplify the right side.

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Step 6.4.1

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

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Step 6.4.1.1

Cancel the common factor of $- 3$ and $3$ .

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Step 6.4.1.1.1

Factor $3$ out of $5 (- 3)$ .

$x = - \frac{3 (5 \cdot (- 1))}{3}$

$z = 3$

$y = - 3$

Step 6.4.1.1.2

Cancel the common factors.

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Step 6.4.1.1.2.1

Factor $3$ out of $3$ .

$x = - \frac{3 (5 \cdot (- 1))}{3 (1)}$

$z = 3$

$y = - 3$

Step 6.4.1.1.2.2

Cancel the common factor.

$x = - \frac{3 (5 \cdot (- 1))}{3 \cdot 1}$

$z = 3$

$y = - 3$

Step 6.4.1.1.2.3

Rewrite the expression.

$x = - \frac{5 \cdot (- 1)}{1}$

$z = 3$

$y = - 3$

Step 6.4.1.1.2.4

Divide $5 \cdot (- 1)$ by $1$ .

$x = - (5 \cdot (- 1))$

$z = 3$

$y = - 3$

$x = - (5 \cdot (- 1))$

$z = 3$

$y = - 3$

$x = - (5 \cdot (- 1))$

$z = 3$

$y = - 3$

Step 6.4.1.2

Multiply $- (5 \cdot (- 1))$ .

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Step 6.4.1.2.1

Multiply $5$ by $- 1$ .

$x = 5$

$z = 3$

$y = - 3$

Step 6.4.1.2.2

Multiply $- 1$ by $- 5$ .

$x = 5$

$z = 3$

$y = - 3$

$x = 5$

$z = 3$

$y = - 3$

$x = 5$

$z = 3$

$y = - 3$

$x = 5$

$z = 3$

$y = - 3$

$x = 5$

$z = 3$

$y = - 3$

Step 7

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

$(5, - 3, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(5, - 3, 3)$

Equation Form:

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