Solve the System of Equations x-y+2z=9 -2x+y+z=-1 2x+2y-z=-5

$x - y + 2 z = 9$ $- 2 x + y + z = - 1$ $2 x + 2 y - z = - 5$

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

Add $y$ to both sides of the equation.

$x + 2 z = 9 + y$

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

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

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

$x = 9 + y - 2 z$

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

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

$x = 9 + y - 2 z$

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

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

Replace all occurrences of $x$ with $9 + y - 2 z$ in each equation.

Replace all occurrences of $x$ in $- 2 x + y + z = - 1$ with $9 + y - 2 z$ .

$- 2 (9 + y - 2 z) + y + z = - 1$

$x = 9 + y - 2 z$

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

Simplify the left side.

Simplify $- 2 (9 + y - 2 z) + y + z$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot 9 - 2 y - 2 (- 2 z) + y + z = - 1$

$x = 9 + y - 2 z$

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

Simplify.

Multiply $- 2$ by $9$ .

$- 18 - 2 y - 2 (- 2 z) + y + z = - 1$

$x = 9 + y - 2 z$

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

Multiply $- 2$ by $- 2$ .

$- 18 - 2 y + 4 z + y + z = - 1$

$x = 9 + y - 2 z$

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

$- 18 - 2 y + 4 z + y + z = - 1$

$x = 9 + y - 2 z$

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

$- 18 - 2 y + 4 z + y + z = - 1$

$x = 9 + y - 2 z$

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

Simplify by adding terms.

Add $- 2 y$ and $y$ .

$- 18 - y + 4 z + z = - 1$

$x = 9 + y - 2 z$

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

Add $4 z$ and $z$ .

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

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

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

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

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

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

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

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

Replace all occurrences of $x$ in $2 x + 2 y - z = - 5$ with $9 + y - 2 z$ .

$2 (9 + y - 2 z) + 2 y - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Simplify the left side.

Simplify $2 (9 + y - 2 z) + 2 y - z$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 9 + 2 y + 2 (- 2 z) + 2 y - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Simplify.

Multiply $2$ by $9$ .

$18 + 2 y + 2 (- 2 z) + 2 y - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Multiply $- 2$ by $2$ .

$18 + 2 y - 4 z + 2 y - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$18 + 2 y - 4 z + 2 y - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$18 + 2 y - 4 z + 2 y - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Simplify by adding terms.

Add $2 y$ and $2 y$ .

$18 + 4 y - 4 z - z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Subtract $z$ from $- 4 z$ .

$18 + 4 y - 5 z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$18 + 4 y - 5 z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$18 + 4 y - 5 z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$18 + 4 y - 5 z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$18 + 4 y - 5 z = - 5$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Solve for $y$ in $18 + 4 y - 5 z = - 5$ .

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

Subtract $18$ from both sides of the equation.

$4 y - 5 z = - 5 - 18$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

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

$4 y = - 5 - 18 + 5 z$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Subtract $18$ from $- 5$ .

$4 y = - 23 + 5 z$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$4 y = - 23 + 5 z$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Divide each term in $4 y = - 23 + 5 z$ by $4$ and simplify.

Divide each term in $4 y = - 23 + 5 z$ by $4$ .

$\frac{4 y}{4} = \frac{- 23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Divide $y$ by $1$ .

$y = \frac{- 23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$y = \frac{- 23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$y = \frac{- 23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$- 18 - y + 5 z = - 1$

$x = 9 + y - 2 z$

Replace all occurrences of $y$ with $- \frac{23}{4} + \frac{5 z}{4}$ in each equation.

Replace all occurrences of $y$ in $- 18 - y + 5 z = - 1$ with $- \frac{23}{4} + \frac{5 z}{4}$ .

$- 18 - (- \frac{23}{4} + \frac{5 z}{4}) + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Simplify the left side.

Simplify $- 18 - (- \frac{23}{4} + \frac{5 z}{4}) + 5 z$ .

Simplify each term.

Apply the distributive property.

$- 18 + \frac{23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Multiply $- - \frac{23}{4}$ .

Multiply $- 1$ by $- 1$ .

$- 18 + 1 (\frac{23}{4}) - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Multiply $\frac{23}{4}$ by $1$ .

$- 18 + \frac{23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

$- 18 + \frac{23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

$- 18 + \frac{23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 18 \cdot \frac{4}{4} + \frac{23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Combine $- 18$ and $\frac{4}{4}$ .

$\frac{- 18 \cdot 4}{4} + \frac{23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Combine the numerators over the common denominator.

$\frac{- 18 \cdot 4 + 23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Simplify the numerator.

Multiply $- 18$ by $4$ .

$\frac{- 72 + 23}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Add $- 72$ and $23$ .

$\frac{- 49}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

$\frac{- 49}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Move the negative in front of the fraction.

$- \frac{49}{4} - \frac{5 z}{4} + 5 z = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

To write $5 z$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{49}{4} - \frac{5 z}{4} + 5 z \cdot \frac{4}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Combine $5 z$ and $\frac{4}{4}$ .

$- \frac{49}{4} - \frac{5 z}{4} + \frac{5 z \cdot 4}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Combine the numerators over the common denominator.

$- \frac{49}{4} + \frac{- 5 z + 5 z \cdot 4}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Combine the numerators over the common denominator.

$\frac{- 49 - 5 z + 5 z \cdot 4}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Multiply $4$ by $5$ .

$\frac{- 49 - 5 z + 20 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Add $- 5 z$ and $20 z$ .

$\frac{- 49 + 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{- 1 \cdot 49 + 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Factor $- 1$ out of $15 z$ .

$\frac{- 1 \cdot 49 - (- 15 z)}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Factor $- 1$ out of $- 1 (49) - (- 15 z)$ .

$\frac{- 1 (49 - 15 z)}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Move the negative in front of the fraction.

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 + y - 2 z$

Replace all occurrences of $y$ in $x = 9 + y - 2 z$ with $- \frac{23}{4} + \frac{5 z}{4}$ .

$x = 9 - \frac{23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify $x = 9 - \frac{23}{4} + \frac{5 z}{4} - 2 z$ .

Simplify the left side.

Remove parentheses.

$x = 9 - \frac{23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 9 - \frac{23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify the right side.

Simplify $9 - \frac{23}{4} + \frac{5 z}{4} - 2 z$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = 9 \cdot \frac{4}{4} - \frac{23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Combine $9$ and $\frac{4}{4}$ .

$x = \frac{9 \cdot 4}{4} - \frac{23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Combine the numerators over the common denominator.

$x = \frac{9 \cdot 4 - 23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify the numerator.

Multiply $9$ by $4$ .

$x = \frac{36 - 23}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Subtract $23$ from $36$ .

$x = \frac{13}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = \frac{13}{4} + \frac{5 z}{4} - 2 z$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

To write $- 2 z$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = \frac{13}{4} + \frac{5 z}{4} - 2 z \cdot \frac{4}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Combine $- 2 z$ and $\frac{4}{4}$ .

$x = \frac{13}{4} + \frac{5 z}{4} + \frac{- 2 z \cdot 4}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Combine the numerators over the common denominator.

$x = \frac{13}{4} + \frac{5 z - 2 z \cdot 4}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Combine the numerators over the common denominator.

$x = \frac{13 + 5 z - 2 z \cdot 4}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Multiply $4$ by $- 2$ .

$x = \frac{13 + 5 z - 8 z}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Subtract $8 z$ from $5 z$ .

$x = \frac{13 - 3 z}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = \frac{13 - 3 z}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = \frac{13 - 3 z}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = \frac{13 - 3 z}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = \frac{13 - 3 z}{4}$

$- \frac{49 - 15 z}{4} = - 1$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Solve for $z$ in $- \frac{49 - 15 z}{4} = - 1$ .

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{49 - 15 z}{4}) = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{49 - 15 z}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{49 - 15 z}{4}$ into the numerator.

$- 4 \frac{- (49 - 15 z)}{4} = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Factor $4$ out of $- 4$ .

$4 (- 1) (\frac{- (49 - 15 z)}{4}) = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Cancel the common factor.

$4 \cdot (- 1 \frac{- (49 - 15 z)}{4}) = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Rewrite the expression.

$49 - 15 z = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$49 - 15 z = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (49 - 15 z) = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Multiply $49 - 15 z$ by $1$ .

$49 - 15 z = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$49 - 15 z = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$49 - 15 z = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$49 - 15 z = - 4 \cdot - 1$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify the right side.

Multiply $- 4$ by $- 1$ .

$49 - 15 z = 4$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$49 - 15 z = 4$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$49 - 15 z = 4$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

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

Subtract $49$ from both sides of the equation.

$- 15 z = 4 - 49$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Subtract $49$ from $4$ .

$- 15 z = - 45$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$- 15 z = - 45$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Divide each term in $- 15 z = - 45$ by $- 15$ and simplify.

Divide each term in $- 15 z = - 45$ by $- 15$ .

$\frac{- 15 z}{- 15} = \frac{- 45}{- 15}$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 z}{- 15} = \frac{- 45}{- 15}$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Divide $z$ by $1$ .

$z = \frac{- 45}{- 15}$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$z = \frac{- 45}{- 15}$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$z = \frac{- 45}{- 15}$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify the right side.

Divide $- 45$ by $- 15$ .

$z = 3$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$z = 3$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$z = 3$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$z = 3$

$x = \frac{13 - 3 z}{4}$

$y = - \frac{23}{4} + \frac{5 z}{4}$

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

Replace all occurrences of $z$ in $x = \frac{13 - 3 z}{4}$ with $3$ .

$x = \frac{13 - 3 \cdot 3}{4}$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Simplify the right side.

Simplify $\frac{13 - 3 \cdot 3}{4}$ .

Simplify the numerator.

Multiply $- 3$ by $3$ .

$x = \frac{13 - 9}{4}$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Subtract $9$ from $13$ .

$x = \frac{4}{4}$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = \frac{4}{4}$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Divide $4$ by $4$ .

$x = 1$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 1$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

$x = 1$

$z = 3$

$y = - \frac{23}{4} + \frac{5 z}{4}$

Replace all occurrences of $z$ in $y = - \frac{23}{4} + \frac{5 z}{4}$ with $3$ .

$y = - \frac{23}{4} + \frac{5 (3)}{4}$

$x = 1$

$z = 3$

Simplify the right side.

Simplify $- \frac{23}{4} + \frac{5 (3)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 23 + 5 (3)}{4}$

$x = 1$

$z = 3$

Simplify the expression.

Multiply $5$ by $3$ .

$y = \frac{- 23 + 15}{4}$

$x = 1$

$z = 3$

Add $- 23$ and $15$ .

$y = \frac{- 8}{4}$

$x = 1$

$z = 3$

Divide $- 8$ by $4$ .

$y = - 2$

$x = 1$

$z = 3$

$y = - 2$

$x = 1$

$z = 3$

$y = - 2$

$x = 1$

$z = 3$

$y = - 2$

$x = 1$

$z = 3$

$y = - 2$

$x = 1$

$z = 3$

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

$(1, - 2, 3)$

The result can be shown in multiple forms.

Point Form:

$(1, - 2, 3)$

Equation Form:

$x = 1, y = - 2, z = 3$

Solve the System of Equations x-y+2z=9 -2x+y+z=-1 2x+2y-z=-5

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