Solve the System of Equations -3x-5y+z=-8 2x+8y-z=-4 x+2y-z=2

$- 3 x - 5 y + z = - 8$ $2 x + 8 y - z = - 4$ $x + 2 y - z = 2$

Step 1

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

Add $3 x$ to both sides of the equation.

$- 5 y + z = - 8 + 3 x$

$2 x + 8 y - z = - 4$

$x + 2 y - z = 2$

Add $5 y$ to both sides of the equation.

$z = - 8 + 3 x + 5 y$

$2 x + 8 y - z = - 4$

$x + 2 y - z = 2$

$z = - 8 + 3 x + 5 y$

$2 x + 8 y - z = - 4$

$x + 2 y - z = 2$

Step 2

Replace all occurrences of $z$ with $- 8 + 3 x + 5 y$ in each equation.

Replace all occurrences of $z$ in $2 x + 8 y - z = - 4$ with $- 8 + 3 x + 5 y$ .

$2 x + 8 y - (- 8 + 3 x + 5 y) = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Simplify the left side.

Simplify $2 x + 8 y - (- 8 + 3 x + 5 y)$ .

Simplify each term.

Apply the distributive property.

$2 x + 8 y + 8 - (3 x) - (5 y) = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Simplify.

Multiply $- 1$ by $- 8$ .

$2 x + 8 y + 8 - (3 x) - (5 y) = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Multiply $3$ by $- 1$ .

$2 x + 8 y + 8 - 3 x - (5 y) = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Multiply $5$ by $- 1$ .

$2 x + 8 y + 8 - 3 x - 5 y = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

$2 x + 8 y + 8 - 3 x - 5 y = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

$2 x + 8 y + 8 - 3 x - 5 y = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Simplify by adding terms.

Subtract $3 x$ from $2 x$ .

$- x + 8 y + 8 - 5 y = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Subtract $5 y$ from $8 y$ .

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y - z = 2$

Replace all occurrences of $z$ in $x + 2 y - z = 2$ with $- 8 + 3 x + 5 y$ .

$x + 2 y - (- 8 + 3 x + 5 y) = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Simplify the left side.

Simplify $x + 2 y - (- 8 + 3 x + 5 y)$ .

Simplify each term.

Apply the distributive property.

$x + 2 y + 8 - (3 x) - (5 y) = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Simplify.

Multiply $- 1$ by $- 8$ .

$x + 2 y + 8 - (3 x) - (5 y) = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Multiply $3$ by $- 1$ .

$x + 2 y + 8 - 3 x - (5 y) = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Multiply $5$ by $- 1$ .

$x + 2 y + 8 - 3 x - 5 y = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y + 8 - 3 x - 5 y = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x + 2 y + 8 - 3 x - 5 y = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Simplify by adding terms.

Subtract $3 x$ from $x$ .

$- 2 x + 2 y + 8 - 5 y = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Subtract $5 y$ from $2 y$ .

$- 2 x - 3 y + 8 = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$- 2 x - 3 y + 8 = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$- 2 x - 3 y + 8 = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$- 2 x - 3 y + 8 = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$- 2 x - 3 y + 8 = 2$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Step 3

Solve for $x$ in $- 2 x - 3 y + 8 = 2$ .

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

Add $3 y$ to both sides of the equation.

$- 2 x + 8 = 2 + 3 y$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Subtract $8$ from both sides of the equation.

$- 2 x = 2 + 3 y - 8$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Subtract $8$ from $2$ .

$- 2 x = 3 y - 6$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$- 2 x = 3 y - 6$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Divide each term in $- 2 x = 3 y - 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = 3 y - 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{3 y}{- 2} + \frac{- 6}{- 2}$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{3 y}{- 2} + \frac{- 6}{- 2}$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Divide $x$ by $1$ .

$x = \frac{3 y}{- 2} + \frac{- 6}{- 2}$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x = \frac{3 y}{- 2} + \frac{- 6}{- 2}$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

$x = \frac{3 y}{- 2} + \frac{- 6}{- 2}$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{3 y}{2} + \frac{- 6}{- 2}$

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Divide $- 6$ by $- 2$ .

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

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

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

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

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

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

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

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

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

$- x + 3 y + 8 = - 4$

$z = - 8 + 3 x + 5 y$

Step 4

Replace all occurrences of $x$ with $- \frac{3 y}{2} + 3$ in each equation.

Replace all occurrences of $x$ in $- x + 3 y + 8 = - 4$ with $- \frac{3 y}{2} + 3$ .

$- (- \frac{3 y}{2} + 3) + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Simplify the left side.

Simplify $- (- \frac{3 y}{2} + 3) + 3 y + 8$ .

Simplify each term.

Apply the distributive property.

$\frac{3 y}{2} - 1 \cdot 3 + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $- - \frac{3 y}{2}$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{3 y}{2}) - 1 \cdot 3 + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $\frac{3 y}{2}$ by $1$ .

$\frac{3 y}{2} - 1 \cdot 3 + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{3 y}{2} - 1 \cdot 3 + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $- 1$ by $3$ .

$\frac{3 y}{2} - 3 + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{3 y}{2} - 3 + 3 y + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 y}{2} + 3 y \cdot \frac{2}{2} - 3 + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

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

$\frac{3 y}{2} + \frac{3 y \cdot 2}{2} - 3 + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Combine the numerators over the common denominator.

$\frac{3 y + 3 y \cdot 2}{2} - 3 + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Find the common denominator.

Write $- 3$ as a fraction with denominator $1$ .

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3}{1} + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $\frac{- 3}{1}$ by $\frac{2}{2}$ .

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3}{1} \cdot \frac{2}{2} + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $\frac{- 3}{1}$ by $\frac{2}{2}$ .

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + 8 = - 4$

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

$z = - 8 + 3 x + 5 y$

Write $8$ as a fraction with denominator $1$ .

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{8}{1} = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{8}{1} \cdot \frac{2}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{8 \cdot 2}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{3 y + 3 y \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{8 \cdot 2}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Combine the numerators over the common denominator.

$\frac{3 y + 3 y \cdot 2 - 3 \cdot 2 + 8 \cdot 2}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Simplify each term.

Multiply $2$ by $3$ .

$\frac{3 y + 6 y - 3 \cdot 2 + 8 \cdot 2}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $- 3$ by $2$ .

$\frac{3 y + 6 y - 6 + 8 \cdot 2}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Multiply $8$ by $2$ .

$\frac{3 y + 6 y - 6 + 16}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{3 y + 6 y - 6 + 16}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Simplify by adding terms.

Add $3 y$ and $6 y$ .

$\frac{9 y - 6 + 16}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Add $- 6$ and $16$ .

$\frac{9 y + 10}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

$z = - 8 + 3 x + 5 y$

Replace all occurrences of $x$ in $z = - 8 + 3 x + 5 y$ with $- \frac{3 y}{2} + 3$ .

$z = - 8 + 3 (- \frac{3 y}{2} + 3) + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

Simplify the right side.

Simplify $- 8 + 3 (- \frac{3 y}{2} + 3) + 5 y$ .

Simplify each term.

Apply the distributive property.

$z = - 8 + 3 (- \frac{3 y}{2}) + 3 \cdot 3 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

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

Multiply $- 1$ by $3$ .

$z = - 8 - 3 \frac{3 y}{2} + 3 \cdot 3 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

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

$z = - 8 + \frac{- 3 (3 y)}{2} + 3 \cdot 3 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

Multiply $3$ by $- 3$ .

$z = - 8 + \frac{- 9 y}{2} + 3 \cdot 3 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

$z = - 8 + \frac{- 9 y}{2} + 3 \cdot 3 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

Multiply $3$ by $3$ .

$z = - 8 + \frac{- 9 y}{2} + 9 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

Move the negative in front of the fraction.

$z = - 8 - \frac{9 y}{2} + 9 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

$z = - 8 - \frac{9 y}{2} + 9 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

Add $- 8$ and $9$ .

$z = - \frac{9 y}{2} + 1 + 5 y$

$\frac{9 y + 10}{2} = - 4$

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

To write $5 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z = - \frac{9 y}{2} + 5 y \cdot \frac{2}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

Simplify terms.

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

$z = - \frac{9 y}{2} + \frac{5 y \cdot 2}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

Combine the numerators over the common denominator.

$z = \frac{- 9 y + 5 y \cdot 2}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

$z = \frac{- 9 y + 5 y \cdot 2}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

Simplify each term.

Simplify the numerator.

Factor $y$ out of $- 9 y + 5 y \cdot 2$ .

Factor $y$ out of $- 9 y$ .

$z = \frac{y \cdot - 9 + 5 y \cdot 2}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

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

$z = \frac{y \cdot - 9 + y (5 \cdot 2)}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

Factor $y$ out of $y \cdot - 9 + y (5 \cdot 2)$ .

$z = \frac{y (- 9 + 5 \cdot 2)}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

$z = \frac{y (- 9 + 5 \cdot 2)}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

Multiply $5$ by $2$ .

$z = \frac{y (- 9 + 10)}{2} + 1$

$\frac{9 y + 10}{2} = - 4$

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

Add $- 9$ and $10$ .

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

$\frac{9 y + 10}{2} = - 4$

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

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

$\frac{9 y + 10}{2} = - 4$

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

Multiply $y$ by $1$ .

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

$\frac{9 y + 10}{2} = - 4$

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

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

$\frac{9 y + 10}{2} = - 4$

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

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

$\frac{9 y + 10}{2} = - 4$

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

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

$\frac{9 y + 10}{2} = - 4$

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

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

$\frac{9 y + 10}{2} = - 4$

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

Step 5

Solve for $y$ in $\frac{9 y + 10}{2} = - 4$ .

Multiply both sides by $2$ .

$\frac{9 y + 10}{2} \cdot 2 = - 4 \cdot 2$

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

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 y + 10}{2} \cdot 2 = - 4 \cdot 2$

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

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

Rewrite the expression.

$9 y + 10 = - 4 \cdot 2$

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

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

$9 y + 10 = - 4 \cdot 2$

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

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

$9 y + 10 = - 4 \cdot 2$

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

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

Simplify the right side.

Multiply $- 4$ by $2$ .

$9 y + 10 = - 8$

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

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

$9 y + 10 = - 8$

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

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

$9 y + 10 = - 8$

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

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

Solve for $y$ .

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

Subtract $10$ from both sides of the equation.

$9 y = - 8 - 10$

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

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

Subtract $10$ from $- 8$ .

$9 y = - 18$

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

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

$9 y = - 18$

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

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

Divide each term in $9 y = - 18$ by $9$ and simplify.

Divide each term in $9 y = - 18$ by $9$ .

$\frac{9 y}{9} = \frac{- 18}{9}$

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

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

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 18}{9}$

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

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

Divide $y$ by $1$ .

$y = \frac{- 18}{9}$

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

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

$y = \frac{- 18}{9}$

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

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

$y = \frac{- 18}{9}$

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

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

Simplify the right side.

Divide $- 18$ by $9$ .

$y = - 2$

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

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

$y = - 2$

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

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

$y = - 2$

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

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

$y = - 2$

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

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

$y = - 2$

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

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

Step 6

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $z = \frac{y}{2} + 1$ with $- 2$ .

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

$y = - 2$

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

Simplify the right side.

Simplify $\frac{- 2}{2} + 1$ .

Divide $- 2$ by $2$ .

$z = - 1 + 1$

$y = - 2$

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

Add $- 1$ and $1$ .

$z = 0$

$y = - 2$

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

$z = 0$

$y = - 2$

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

$z = 0$

$y = - 2$

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

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

$x = - \frac{3 (- 2)}{2} + 3$

$z = 0$

$y = - 2$

Simplify the right side.

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

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

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

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

$z = 0$

$y = - 2$

Cancel the common factors.

Factor $2$ out of $2$ .

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

$z = 0$

$y = - 2$

Cancel the common factor.

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

$z = 0$

$y = - 2$

Rewrite the expression.

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

$z = 0$

$y = - 2$

Divide $3 \cdot (- 1)$ by $1$ .

$x = - (3 \cdot (- 1)) + 3$

$z = 0$

$y = - 2$

$x = - (3 \cdot (- 1)) + 3$

$z = 0$

$y = - 2$

$x = - (3 \cdot (- 1)) + 3$

$z = 0$

$y = - 2$

Multiply $- (3 \cdot (- 1))$ .

Multiply $3$ by $- 1$ .

$x = 3 + 3$

$z = 0$

$y = - 2$

Multiply $- 1$ by $- 3$ .

$x = 3 + 3$

$z = 0$

$y = - 2$

$x = 3 + 3$

$z = 0$

$y = - 2$

$x = 3 + 3$

$z = 0$

$y = - 2$

Add $3$ and $3$ .

$x = 6$

$z = 0$

$y = - 2$

$x = 6$

$z = 0$

$y = - 2$

$x = 6$

$z = 0$

$y = - 2$

$x = 6$

$z = 0$

$y = - 2$

Step 7

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

$(6, - 2, 0)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(6, - 2, 0)$

Equation Form:

$x = 6, y = - 2, z = 0$

Solve the System of Equations -3x-5y+z=-8 2x+8y-z=-4 x+2y-z=2

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