Solve the System of Equations -4x-5y-z=18 -2x-5y-2z=12 -2x+5y+2z=4

$- 4 x - 5 y - z = 18$ $- 2 x - 5 y - 2 z = 12$ $- 2 x + 5 y + 2 z = 4$

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

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

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

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

$- 2 x - 5 y - 2 z = 12$

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

Add $z$ to both sides of the equation.

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

Divide each term in $- 4 x = 18 + 5 y + z$ by $- 4$ and simplify.

Divide each term in $- 4 x = 18 + 5 y + z$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{18}{- 4} + \frac{5 y}{- 4} + \frac{z}{- 4}$

$- 2 x - 5 y - 2 z = 12$

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{18}{- 4} + \frac{5 y}{- 4} + \frac{z}{- 4}$

$- 2 x - 5 y - 2 z = 12$

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

Divide $x$ by $1$ .

$x = \frac{18}{- 4} + \frac{5 y}{- 4} + \frac{z}{- 4}$

$- 2 x - 5 y - 2 z = 12$

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

$x = \frac{18}{- 4} + \frac{5 y}{- 4} + \frac{z}{- 4}$

$- 2 x - 5 y - 2 z = 12$

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

$x = \frac{18}{- 4} + \frac{5 y}{- 4} + \frac{z}{- 4}$

$- 2 x - 5 y - 2 z = 12$

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $18$ and $- 4$ .

Factor $2$ out of $18$ .

$x = \frac{2 (9)}{- 4} + \frac{5 y}{- 4} + \frac{z}{- 4}$

$- 2 x - 5 y - 2 z = 12$

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

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

$- 2 x - 5 y - 2 z = 12$

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

Cancel the common factor.

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

$- 2 x - 5 y - 2 z = 12$

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

Rewrite the expression.

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

Move the negative in front of the fraction.

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

$- 2 x - 5 y - 2 z = 12$

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

Move the negative in front of the fraction.

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

$- 2 x - 5 y - 2 z = 12$

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

Move the negative in front of the fraction.

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

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

$- 2 x - 5 y - 2 z = 12$

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

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

Replace all occurrences of $x$ in $- 2 x - 5 y - 2 z = 12$ with $- \frac{9}{2} - \frac{5 y}{4} - \frac{z}{4}$ .

$- 2 (- \frac{9}{2} - \frac{5 y}{4} - \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Simplify the left side.

Simplify $- 2 (- \frac{9}{2} - \frac{5 y}{4} - \frac{z}{4}) - 5 y - 2 z$ .

Simplify each term.

Apply the distributive property.

$- 2 (- \frac{9}{2}) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Simplify.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$- 2 (\frac{- 9}{2}) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- 9}{2}) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Cancel the common factor.

$2 \cdot (- 1 (\frac{- 9}{2})) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Rewrite the expression.

$- 1 \cdot - 9 - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

$- 1 \cdot - 9 - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Multiply $- 1$ by $- 9$ .

$9 - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 y}{4}$ into the numerator.

$9 - 2 \frac{- 5 y}{4} - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Factor $2$ out of $- 2$ .

$9 + 2 (- 1) (\frac{- 5 y}{4}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Factor $2$ out of $4$ .

$9 + 2 \cdot (- 1 \frac{- 5 y}{2 \cdot 2}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Cancel the common factor.

$9 + 2 \cdot (- 1 \frac{- 5 y}{2 \cdot 2}) - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Rewrite the expression.

$9 - 1 \frac{- 5 y}{2} - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

$9 - 1 \frac{- 5 y}{2} - 2 (- \frac{z}{4}) - 5 y - 2 z = 12$

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

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

Cancel the common factor of $2$ .

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

$9 - 1 \frac{- 5 y}{2} - 2 \frac{- z}{4} - 5 y - 2 z = 12$

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

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

Factor $2$ out of $- 2$ .

$9 - 1 \frac{- 5 y}{2} + 2 (- 1) (\frac{- z}{4}) - 5 y - 2 z = 12$

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

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

Factor $2$ out of $4$ .

$9 - 1 \frac{- 5 y}{2} + 2 \cdot (- 1 \frac{- z}{2 \cdot 2}) - 5 y - 2 z = 12$

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

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

Cancel the common factor.

$9 - 1 \frac{- 5 y}{2} + 2 \cdot (- 1 \frac{- z}{2 \cdot 2}) - 5 y - 2 z = 12$

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

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

Rewrite the expression.

$9 - 1 \frac{- 5 y}{2} - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

$9 - 1 \frac{- 5 y}{2} - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

$9 - 1 \frac{- 5 y}{2} - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

Simplify each term.

Move the negative in front of the fraction.

$9 - 1 (- \frac{(5) y}{2}) - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

Multiply $- 1 (- \frac{5 y}{2})$ .

Multiply $- 1$ by $- 1$ .

$9 + 1 (\frac{5 y}{2}) - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

Multiply $\frac{5 y}{2}$ by $1$ .

$9 + \frac{5 y}{2} - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

$9 + \frac{5 y}{2} - 1 \frac{- z}{2} - 5 y - 2 z = 12$

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

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

Move the negative in front of the fraction.

$9 + \frac{5 y}{2} - 1 (- \frac{z}{2}) - 5 y - 2 z = 12$

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

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

Multiply $- 1 (- \frac{z}{2})$ .

Multiply $- 1$ by $- 1$ .

$9 + \frac{5 y}{2} + 1 (\frac{z}{2}) - 5 y - 2 z = 12$

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

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

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

$9 + \frac{5 y}{2} + \frac{z}{2} - 5 y - 2 z = 12$

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

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

$9 + \frac{5 y}{2} + \frac{z}{2} - 5 y - 2 z = 12$

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

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

$9 + \frac{5 y}{2} + \frac{z}{2} - 5 y - 2 z = 12$

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

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

$9 + \frac{5 y}{2} + \frac{z}{2} - 5 y - 2 z = 12$

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

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

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

$9 + \frac{z}{2} + \frac{5 y}{2} - 5 y \cdot \frac{2}{2} - 2 z = 12$

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

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

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

$9 + \frac{z}{2} + \frac{5 y}{2} + \frac{- 5 y \cdot 2}{2} - 2 z = 12$

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

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

Combine the numerators over the common denominator.

$9 + \frac{z}{2} + \frac{5 y - 5 y \cdot 2}{2} - 2 z = 12$

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

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

Combine the numerators over the common denominator.

$9 - 2 z + \frac{z + 5 y - 5 y \cdot 2}{2} = 12$

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

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

Multiply $2$ by $- 5$ .

$9 - 2 z + \frac{z + 5 y - 10 y}{2} = 12$

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

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

Subtract $10 y$ from $5 y$ .

$9 - 2 z + \frac{z - 5 y}{2} = 12$

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

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

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 z + 9 \cdot \frac{2}{2} + \frac{z - 5 y}{2} = 12$

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

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

Combine $9$ and $\frac{2}{2}$ .

$- 2 z + \frac{9 \cdot 2}{2} + \frac{z - 5 y}{2} = 12$

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

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

Combine the numerators over the common denominator.

$- 2 z + \frac{9 \cdot 2 + z - 5 y}{2} = 12$

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

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

Multiply $9$ by $2$ .

$- 2 z + \frac{18 + z - 5 y}{2} = 12$

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

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

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

$- 2 z \cdot \frac{2}{2} + \frac{18 + z - 5 y}{2} = 12$

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

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

Simplify terms.

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

$\frac{- 2 z \cdot 2}{2} + \frac{18 + z - 5 y}{2} = 12$

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

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

Combine the numerators over the common denominator.

$\frac{- 2 z \cdot 2 + 18 + z - 5 y}{2} = 12$

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

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

$\frac{- 2 z \cdot 2 + 18 + z - 5 y}{2} = 12$

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

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

Simplify the numerator.

Multiply $2$ by $- 2$ .

$\frac{- 4 z + 18 + z - 5 y}{2} = 12$

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

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

Add $- 4 z$ and $z$ .

$\frac{- 3 z + 18 - 5 y}{2} = 12$

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

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

$\frac{- 3 z + 18 - 5 y}{2} = 12$

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

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

Simplify with factoring out.

Factor $- 1$ out of $- 3 z$ .

$\frac{- (3 z) + 18 - 5 y}{2} = 12$

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

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

Rewrite $18$ as $- 1 (- 18)$ .

$\frac{- (3 z) - 1 \cdot - 18 - 5 y}{2} = 12$

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

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

Factor $- 1$ out of $- (3 z) - 1 (- 18)$ .

$\frac{- (3 z - 18) - 5 y}{2} = 12$

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

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

Factor $- 1$ out of $- 5 y$ .

$\frac{- (3 z - 18) - (5 y)}{2} = 12$

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

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

Factor $- 1$ out of $- (3 z - 18) - (5 y)$ .

$\frac{- (3 z - 18 + 5 y)}{2} = 12$

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

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

Simplify the expression.

Rewrite $- (3 z - 18 + 5 y)$ as $- 1 (3 z - 18 + 5 y)$ .

$\frac{- 1 (3 z - 18 + 5 y)}{2} = 12$

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

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

Move the negative in front of the fraction.

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

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

$- 2 (- \frac{9}{2} - \frac{5 y}{4} - \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify the left side.

Simplify $- 2 (- \frac{9}{2} - \frac{5 y}{4} - \frac{z}{4}) + 5 y + 2 z$ .

Simplify each term.

Apply the distributive property.

$- 2 (- \frac{9}{2}) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$- 2 (\frac{- 9}{2}) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- 9}{2}) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factor.

$2 \cdot (- 1 (\frac{- 9}{2})) - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Rewrite the expression.

$- 1 \cdot - 9 - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$- 1 \cdot - 9 - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Multiply $- 1$ by $- 9$ .

$9 - 2 (- \frac{5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 y}{4}$ into the numerator.

$9 - 2 \frac{- 5 y}{4} - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Factor $2$ out of $- 2$ .

$9 + 2 (- 1) (\frac{- 5 y}{4}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Factor $2$ out of $4$ .

$9 + 2 \cdot (- 1 \frac{- 5 y}{2 \cdot 2}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factor.

$9 + 2 \cdot (- 1 \frac{- 5 y}{2 \cdot 2}) - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Rewrite the expression.

$9 - 1 \frac{- 5 y}{2} - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 - 1 \frac{- 5 y}{2} - 2 (- \frac{z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factor of $2$ .

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

$9 - 1 \frac{- 5 y}{2} - 2 \frac{- z}{4} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Factor $2$ out of $- 2$ .

$9 - 1 \frac{- 5 y}{2} + 2 (- 1) (\frac{- z}{4}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Factor $2$ out of $4$ .

$9 - 1 \frac{- 5 y}{2} + 2 \cdot (- 1 \frac{- z}{2 \cdot 2}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factor.

$9 - 1 \frac{- 5 y}{2} + 2 \cdot (- 1 \frac{- z}{2 \cdot 2}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Rewrite the expression.

$9 - 1 \frac{- 5 y}{2} - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 - 1 \frac{- 5 y}{2} - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 - 1 \frac{- 5 y}{2} - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify each term.

Move the negative in front of the fraction.

$9 - 1 (- \frac{(5) y}{2}) - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Multiply $- 1 (- \frac{5 y}{2})$ .

Multiply $- 1$ by $- 1$ .

$9 + 1 (\frac{5 y}{2}) - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Multiply $\frac{5 y}{2}$ by $1$ .

$9 + \frac{5 y}{2} - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 + \frac{5 y}{2} - 1 \frac{- z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Move the negative in front of the fraction.

$9 + \frac{5 y}{2} - 1 (- \frac{z}{2}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Multiply $- 1 (- \frac{z}{2})$ .

Multiply $- 1$ by $- 1$ .

$9 + \frac{5 y}{2} + 1 (\frac{z}{2}) + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$9 + \frac{5 y}{2} + \frac{z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 + \frac{5 y}{2} + \frac{z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 + \frac{5 y}{2} + \frac{z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$9 + \frac{5 y}{2} + \frac{z}{2} + 5 y + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$9 + \frac{z}{2} + \frac{5 y}{2} + 5 y \cdot \frac{2}{2} + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$9 + \frac{z}{2} + \frac{5 y}{2} + \frac{5 y \cdot 2}{2} + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Combine the numerators over the common denominator.

$9 + \frac{z}{2} + \frac{5 y + 5 y \cdot 2}{2} + 2 z = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Combine the numerators over the common denominator.

$9 + 2 z + \frac{z + 5 y + 5 y \cdot 2}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Multiply $2$ by $5$ .

$9 + 2 z + \frac{z + 5 y + 10 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Add $5 y$ and $10 y$ .

$9 + 2 z + \frac{z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 z + 9 \cdot \frac{2}{2} + \frac{z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Combine $9$ and $\frac{2}{2}$ .

$2 z + \frac{9 \cdot 2}{2} + \frac{z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Combine the numerators over the common denominator.

$2 z + \frac{9 \cdot 2 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Multiply $9$ by $2$ .

$2 z + \frac{18 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$2 z \cdot \frac{2}{2} + \frac{18 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify terms.

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

$\frac{2 z \cdot 2}{2} + \frac{18 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Combine the numerators over the common denominator.

$\frac{2 z \cdot 2 + 18 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$\frac{2 z \cdot 2 + 18 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 z + 18 + z + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Add $4 z$ and $z$ .

$\frac{5 z + 18 + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$\frac{5 z + 18 + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$\frac{5 z + 18 + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$\frac{5 z + 18 + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$\frac{5 z + 18 + 15 y}{2} = 4$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Solve for $z$ in $\frac{5 z + 18 + 15 y}{2} = 4$ .

Multiply both sides by $2$ .

$\frac{5 z + 18 + 15 y}{2} \cdot 2 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify.

Simplify the left side.

Simplify $\frac{5 z + 18 + 15 y}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 z + 18 + 15 y}{2} \cdot 2 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Rewrite the expression.

$5 z + 18 + 15 y = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$5 z + 18 + 15 y = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify the expression.

Move $18$ .

$5 z + 15 y + 18 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Reorder $5 z$ and $15 y$ .

$15 y + 5 z + 18 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$15 y + 5 z + 18 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$15 y + 5 z + 18 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$15 y + 5 z + 18 = 4 \cdot 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify the right side.

Multiply $4$ by $2$ .

$15 y + 5 z + 18 = 8$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$15 y + 5 z + 18 = 8$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$15 y + 5 z + 18 = 8$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Solve for $z$ .

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

Subtract $15 y$ from both sides of the equation.

$5 z + 18 = 8 - 15 y$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Subtract $18$ from both sides of the equation.

$5 z = 8 - 15 y - 18$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Subtract $18$ from $8$ .

$5 z = - 15 y - 10$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$5 z = - 15 y - 10$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Divide each term in $5 z = - 15 y - 10$ by $5$ and simplify.

Divide each term in $5 z = - 15 y - 10$ by $5$ .

$\frac{5 z}{5} = \frac{- 15 y}{5} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 z}{5} = \frac{- 15 y}{5} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Divide $z$ by $1$ .

$z = \frac{- 15 y}{5} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = \frac{- 15 y}{5} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = \frac{- 15 y}{5} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 15$ and $5$ .

Factor $5$ out of $- 15 y$ .

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factors.

Factor $5$ out of $5$ .

$z = \frac{5 (- 3 y)}{5 (1)} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Cancel the common factor.

$z = \frac{5 (- 3 y)}{5 \cdot 1} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Rewrite the expression.

$z = \frac{- 3 y}{1} + \frac{- 10}{5}$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Divide $- 3 y$ by $1$ .

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

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

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Divide $- 10$ by $5$ .

$z = - 3 y - 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = - 3 y - 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = - 3 y - 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = - 3 y - 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = - 3 y - 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

$z = - 3 y - 2$

$- \frac{3 z - 18 + 5 y}{2} = 12$

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

Replace all occurrences of $z$ with $- 3 y - 2$ in each equation.

Replace all occurrences of $z$ in $- \frac{3 z - 18 + 5 y}{2} = 12$ with $- 3 y - 2$ .

$- \frac{3 (- 3 y - 2) - 18 + 5 y}{2} = 12$

$z = - 3 y - 2$

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

Simplify the left side.

Simplify $- \frac{3 (- 3 y - 2) - 18 + 5 y}{2}$ .

Simplify the numerator.

Apply the distributive property.

$- \frac{3 (- 3 y) + 3 \cdot - 2 - 18 + 5 y}{2} = 12$

$z = - 3 y - 2$

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

Multiply $- 3$ by $3$ .

$- \frac{- 9 y + 3 \cdot - 2 - 18 + 5 y}{2} = 12$

$z = - 3 y - 2$

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

Multiply $3$ by $- 2$ .

$- \frac{- 9 y - 6 - 18 + 5 y}{2} = 12$

$z = - 3 y - 2$

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

Add $- 9 y$ and $5 y$ .

$- \frac{- 4 y - 6 - 18}{2} = 12$

$z = - 3 y - 2$

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

Subtract $18$ from $- 6$ .

$- \frac{- 4 y - 24}{2} = 12$

$z = - 3 y - 2$

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

Factor $4$ out of $- 4 y - 24$ .

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

$- \frac{4 (- y) - 24}{2} = 12$

$z = - 3 y - 2$

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

Factor $4$ out of $- 24$ .

$- \frac{4 (- y) + 4 (- 6)}{2} = 12$

$z = - 3 y - 2$

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

Factor $4$ out of $4 (- y) + 4 (- 6)$ .

$- \frac{4 (- y - 6)}{2} = 12$

$z = - 3 y - 2$

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

$- \frac{4 (- y - 6)}{2} = 12$

$z = - 3 y - 2$

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

$- \frac{4 (- y - 6)}{2} = 12$

$z = - 3 y - 2$

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

Simplify terms.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 (- y - 6)$ .

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

$z = - 3 y - 2$

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

Cancel the common factors.

Factor $2$ out of $2$ .

$- \frac{2 (2 (- y - 6))}{2 (1)} = 12$

$z = - 3 y - 2$

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

Cancel the common factor.

$- \frac{2 (2 (- y - 6))}{2 \cdot 1} = 12$

$z = - 3 y - 2$

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

Rewrite the expression.

$- \frac{2 (- y - 6)}{1} = 12$

$z = - 3 y - 2$

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

Divide $2 (- y - 6)$ by $1$ .

$- (2 (- y - 6)) = 12$

$z = - 3 y - 2$

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

$- (2 (- y - 6)) = 12$

$z = - 3 y - 2$

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

$- (2 (- y - 6)) = 12$

$z = - 3 y - 2$

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

Apply the distributive property.

$- (2 (- y) + 2 \cdot - 6) = 12$

$z = - 3 y - 2$

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

Multiply.

Multiply $- 1$ by $2$ .

$- (- 2 y + 2 \cdot - 6) = 12$

$z = - 3 y - 2$

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

Multiply $2$ by $- 6$ .

$- (- 2 y - 12) = 12$

$z = - 3 y - 2$

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

$- (- 2 y - 12) = 12$

$z = - 3 y - 2$

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

Apply the distributive property.

$- (- 2 y) + 12 = 12$

$z = - 3 y - 2$

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

Multiply.

Multiply $- 2$ by $- 1$ .

$2 y + 12 = 12$

$z = - 3 y - 2$

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

Multiply $- 1$ by $- 12$ .

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

Replace all occurrences of $z$ in $x = - \frac{9}{2} - \frac{5 y}{4} - \frac{z}{4}$ with $- 3 y - 2$ .

$x = - \frac{9}{2} - \frac{5 y}{4} - \frac{- 3 y - 2}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Simplify the right side.

Simplify $- \frac{9}{2} - \frac{5 y}{4} - \frac{- 3 y - 2}{4}$ .

Combine the numerators over the common denominator.

$x = \frac{- 9}{2} + \frac{- 5 y - (- 3 y - 2)}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Simplify each term.

Apply the distributive property.

$x = \frac{- 9}{2} + \frac{- 5 y - (- 3 y) + 2}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Multiply $- 3$ by $- 1$ .

$x = \frac{- 9}{2} + \frac{- 5 y + 3 y + 2}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Multiply $- 1$ by $- 2$ .

$x = \frac{- 9}{2} + \frac{- 5 y + 3 y + 2}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

$x = \frac{- 9}{2} + \frac{- 5 y + 3 y + 2}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Add $- 5 y$ and $3 y$ .

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Simplify each term.

Move the negative in front of the fraction.

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Cancel the common factor of $- 2 y + 2$ and $4$ .

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

$x = - \frac{9}{2} + \frac{2 (- y) + 2}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Factor $2$ out of $2$ .

$x = - \frac{9}{2} + \frac{2 (- y) + 2 (1)}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Factor $2$ out of $2 (- y) + 2 (1)$ .

$x = - \frac{9}{2} + \frac{2 (- y + 1)}{4}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Cancel the common factors.

Factor $2$ out of $4$ .

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Cancel the common factor.

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Rewrite the expression.

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Simplify terms.

Combine the numerators over the common denominator.

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Add $- 9$ and $1$ .

$x = \frac{- y - 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

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

$x = \frac{- (y) - 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Rewrite $- 8$ as $- 1 (8)$ .

$x = \frac{- (y) - 1 \cdot 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Factor $- 1$ out of $- (y) - 1 (8)$ .

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

$2 y + 12 = 12$

$z = - 3 y - 2$

Simplify the expression.

Rewrite $- (y + 8)$ as $- 1 (y + 8)$ .

$x = \frac{- 1 (y + 8)}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Move the negative in front of the fraction.

$x = - \frac{y + 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

$x = - \frac{y + 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

$x = - \frac{y + 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

$x = - \frac{y + 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

$x = - \frac{y + 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

$x = - \frac{y + 8}{2}$

$2 y + 12 = 12$

$z = - 3 y - 2$

Solve for $y$ in $2 y + 12 = 12$ .

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

Subtract $12$ from both sides of the equation.

$2 y = 12 - 12$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

Subtract $12$ from $12$ .

$2 y = 0$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

$2 y = 0$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

Divide each term in $2 y = 0$ by $2$ and simplify.

Divide each term in $2 y = 0$ by $2$ .

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

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

Divide $y$ by $1$ .

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

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

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

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

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

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

Simplify the right side.

Divide $0$ by $2$ .

$y = 0$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

$y = 0$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

$y = 0$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

$y = 0$

$x = - \frac{y + 8}{2}$

$z = - 3 y - 2$

Replace all occurrences of $y$ with $0$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{y + 8}{2}$ with $0$ .

$x = - \frac{(0) + 8}{2}$

$y = 0$

$z = - 3 y - 2$

Simplify the right side.

Simplify $- \frac{(0) + 8}{2}$ .

Cancel the common factor of $(0) + 8$ and $2$ .

Factor $2$ out of $0$ .

$x = - \frac{2 \cdot 0 + 8}{2}$

$y = 0$

$z = - 3 y - 2$

Factor $2$ out of $8$ .

$x = - \frac{2 \cdot 0 + 2 \cdot 4}{2}$

$y = 0$

$z = - 3 y - 2$

Factor $2$ out of $2 \cdot 0 + 2 \cdot 4$ .

$x = - \frac{2 \cdot (0 + 4)}{2}$

$y = 0$

$z = - 3 y - 2$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = - \frac{2 \cdot (0 + 4)}{2 (1)}$

$y = 0$

$z = - 3 y - 2$

Cancel the common factor.

$x = - \frac{2 \cdot (0 + 4)}{2 \cdot 1}$

$y = 0$

$z = - 3 y - 2$

Rewrite the expression.

$x = - \frac{0 + 4}{1}$

$y = 0$

$z = - 3 y - 2$

Divide $0 + 4$ by $1$ .

$x = - (0 + 4)$

$y = 0$

$z = - 3 y - 2$

$x = - (0 + 4)$

$y = 0$

$z = - 3 y - 2$

$x = - (0 + 4)$

$y = 0$

$z = - 3 y - 2$

Simplify the expression.

Add $0$ and $4$ .

$x = - 1 \cdot 4$

$y = 0$

$z = - 3 y - 2$

Multiply $- 1$ by $4$ .

$x = - 4$

$y = 0$

$z = - 3 y - 2$

$x = - 4$

$y = 0$

$z = - 3 y - 2$

$x = - 4$

$y = 0$

$z = - 3 y - 2$

$x = - 4$

$y = 0$

$z = - 3 y - 2$

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

$z = - 3 \cdot 0 - 2$

$x = - 4$

$y = 0$

Simplify the right side.

Simplify $- 3 \cdot 0 - 2$ .

Multiply $- 3$ by $0$ .

$z = 0 - 2$

$x = - 4$

$y = 0$

Subtract $2$ from $0$ .

$z = - 2$

$x = - 4$

$y = 0$

$z = - 2$

$x = - 4$

$y = 0$

$z = - 2$

$x = - 4$

$y = 0$

$z = - 2$

$x = - 4$

$y = 0$

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

$(- 4, 0, - 2)$

The result can be shown in multiple forms.

Point Form:

$(- 4, 0, - 2)$

Equation Form:

$x = - 4, y = 0, z = - 2$

Solve the System of Equations -4x-5y-z=18 -2x-5y-2z=12 -2x+5y+2z=4

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