Solve the System of Equations -x-2y=-4z+12 3x-6y+z=15 2x+5y+1=0

$- x - 2 y = - 4 z + 12$ $3 x - 6 y + z = 15$ $2 x + 5 y + 1 = 0$

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

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

$- 6 y + z = 15 - 3 x$

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

$2 x + 5 y + 1 = 0$

Add $6 y$ to both sides of the equation.

$z = 15 - 3 x + 6 y$

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

$2 x + 5 y + 1 = 0$

$z = 15 - 3 x + 6 y$

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

$2 x + 5 y + 1 = 0$

Replace all occurrences of $z$ with $15 - 3 x + 6 y$ in each equation.

Replace all occurrences of $z$ in $- x - 2 y = - 4 z + 12$ with $15 - 3 x + 6 y$ .

$- x - 2 y = - 4 (15 - 3 x + 6 y) + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

Simplify the right side.

Simplify $- 4 (15 - 3 x + 6 y) + 12$ .

Simplify each term.

Apply the distributive property.

$- x - 2 y = - 4 \cdot 15 - 4 (- 3 x) - 4 (6 y) + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

Simplify.

Multiply $- 4$ by $15$ .

$- x - 2 y = - 60 - 4 (- 3 x) - 4 (6 y) + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

Multiply $- 3$ by $- 4$ .

$- x - 2 y = - 60 + 12 x - 4 (6 y) + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

Multiply $6$ by $- 4$ .

$- x - 2 y = - 60 + 12 x - 24 y + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

$- x - 2 y = - 60 + 12 x - 24 y + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

$- x - 2 y = - 60 + 12 x - 24 y + 12$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

Add $- 60$ and $12$ .

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$2 x + 5 y + 1 = 0$

Solve for $x$ in $2 x + 5 y + 1 = 0$ .

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

Subtract $5 y$ from both sides of the equation.

$2 x + 1 = - 5 y$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Subtract $1$ from both sides of the equation.

$2 x = - 5 y - 1$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$2 x = - 5 y - 1$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Divide each term in $2 x = - 5 y - 1$ by $2$ and simplify.

Divide each term in $2 x = - 5 y - 1$ by $2$ .

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

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Divide $x$ by $1$ .

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

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

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

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

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

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{(5) y}{2} + \frac{- 1}{2}$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Move the negative in front of the fraction.

$x = - \frac{5 y}{2} - \frac{1}{2}$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$- x - 2 y = 12 x - 24 y - 48$

$z = 15 - 3 x + 6 y$

Replace all occurrences of $x$ with $- \frac{5 y}{2} - \frac{1}{2}$ in each equation.

Replace all occurrences of $x$ in $- x - 2 y = 12 x - 24 y - 48$ with $- \frac{5 y}{2} - \frac{1}{2}$ .

$- (- \frac{5 y}{2} - \frac{1}{2}) - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Simplify $- (- \frac{5 y}{2} - \frac{1}{2}) - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$ .

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$\frac{5 y}{2} + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Multiply $- - \frac{5 y}{2}$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{5 y}{2}) + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

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

$\frac{5 y}{2} + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{5 y}{2} + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

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

Multiply $- 1$ by $- 1$ .

$\frac{5 y}{2} + 1 (\frac{1}{2}) - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

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

$\frac{5 y}{2} + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{5 y}{2} + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{5 y}{2} + \frac{1}{2} - 2 y = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

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

$\frac{5 y}{2} - 2 y \cdot \frac{2}{2} + \frac{1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

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

$\frac{5 y}{2} + \frac{- 2 y \cdot 2}{2} + \frac{1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Combine the numerators over the common denominator.

$\frac{5 y - 2 y \cdot 2}{2} + \frac{1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Combine the numerators over the common denominator.

$\frac{5 y - 2 y \cdot 2 + 1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Multiply $2$ by $- 2$ .

$\frac{5 y - 4 y + 1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Subtract $4 y$ from $5 y$ .

$\frac{y + 1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = 12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Simplify the right side.

Simplify $12 (- \frac{5 y}{2} - \frac{1}{2}) - 24 y - 48$ .

Simplify each term.

Apply the distributive property.

$\frac{y + 1}{2} = 12 (- \frac{5 y}{2}) + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 y}{2}$ into the numerator.

$\frac{y + 1}{2} = 12 (\frac{- 5 y}{2}) + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Factor $2$ out of $12$ .

$\frac{y + 1}{2} = 2 (6) (\frac{- 5 y}{2}) + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Cancel the common factor.

$\frac{y + 1}{2} = 2 \cdot (6 (\frac{- 5 y}{2})) + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Rewrite the expression.

$\frac{y + 1}{2} = 6 (- 5 y) + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = 6 (- 5 y) + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Multiply $- 5$ by $6$ .

$\frac{y + 1}{2} = - 30 y + 12 (- \frac{1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{y + 1}{2} = - 30 y + 12 (\frac{- 1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Factor $2$ out of $12$ .

$\frac{y + 1}{2} = - 30 y + 2 (6) (\frac{- 1}{2}) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Cancel the common factor.

$\frac{y + 1}{2} = - 30 y + 2 \cdot (6 (\frac{- 1}{2})) - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Rewrite the expression.

$\frac{y + 1}{2} = - 30 y + 6 \cdot - 1 - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = - 30 y + 6 \cdot - 1 - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Multiply $6$ by $- 1$ .

$\frac{y + 1}{2} = - 30 y - 6 - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = - 30 y - 6 - 24 y - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Simplify by adding terms.

Subtract $24 y$ from $- 30 y$ .

$\frac{y + 1}{2} = - 54 y - 6 - 48$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Subtract $48$ from $- 6$ .

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 - 3 x + 6 y$

Replace all occurrences of $x$ in $z = 15 - 3 x + 6 y$ with $- \frac{5 y}{2} - \frac{1}{2}$ .

$z = 15 - 3 (- \frac{5 y}{2} - \frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the right side.

Simplify $15 - 3 (- \frac{5 y}{2} - \frac{1}{2}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$z = 15 - 3 (- \frac{5 y}{2}) - 3 (- \frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

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

Multiply $- 1$ by $- 3$ .

$z = 15 + 3 (\frac{5 y}{2}) - 3 (- \frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

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

$z = 15 + \frac{3 (5 y)}{2} - 3 (- \frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Multiply $5$ by $3$ .

$z = 15 + \frac{15 y}{2} - 3 (- \frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 + \frac{15 y}{2} - 3 (- \frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

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

Multiply $- 1$ by $- 3$ .

$z = 15 + \frac{15 y}{2} + 3 (\frac{1}{2}) + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Combine $3$ and $\frac{1}{2}$ .

$z = 15 + \frac{15 y}{2} + \frac{3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 + \frac{15 y}{2} + \frac{3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 15 + \frac{15 y}{2} + \frac{3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

To write $15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z = \frac{15 y}{2} + 15 \cdot \frac{2}{2} + \frac{3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Combine $15$ and $\frac{2}{2}$ .

$z = \frac{15 y}{2} + \frac{15 \cdot 2}{2} + \frac{3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$z = \frac{15 y}{2} + \frac{15 \cdot 2 + 3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the numerator.

Multiply $15$ by $2$ .

$z = \frac{15 y}{2} + \frac{30 + 3}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Add $30$ and $3$ .

$z = \frac{15 y}{2} + \frac{33}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = \frac{15 y}{2} + \frac{33}{2} + 6 y$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z = \frac{15 y}{2} + 6 y \cdot \frac{2}{2} + \frac{33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Combine $6 y$ and $\frac{2}{2}$ .

$z = \frac{15 y}{2} + \frac{6 y \cdot 2}{2} + \frac{33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$z = \frac{15 y + 6 y \cdot 2}{2} + \frac{33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$z = \frac{15 y + 6 y \cdot 2 + 33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Multiply $2$ by $6$ .

$z = \frac{15 y + 12 y + 33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Add $15 y$ and $12 y$ .

$z = \frac{27 y + 33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Factor $3$ out of $27 y + 33$ .

Factor $3$ out of $27 y$ .

$z = \frac{3 (9 y) + 33}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Factor $3$ out of $33$ .

$z = \frac{3 (9 y) + 3 (11)}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Factor $3$ out of $3 (9 y) + 3 (11)$ .

$z = \frac{3 (9 y + 11)}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = \frac{3 (9 y + 11)}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = \frac{3 (9 y + 11)}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = \frac{3 (9 y + 11)}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = \frac{3 (9 y + 11)}{2}$

$\frac{y + 1}{2} = - 54 y - 54$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Solve for $y$ in $\frac{y + 1}{2} = - 54 y - 54$ .

Multiply both sides by $2$ .

$\frac{y + 1}{2} \cdot 2 = (- 54 y - 54) \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{y + 1}{2} \cdot 2 = (- 54 y - 54) \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Rewrite the expression.

$y + 1 = (- 54 y - 54) \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y + 1 = (- 54 y - 54) \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y + 1 = (- 54 y - 54) \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the right side.

Simplify $(- 54 y - 54) \cdot 2$ .

Apply the distributive property.

$y + 1 = - 54 y \cdot 2 - 54 \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Multiply.

Multiply $2$ by $- 54$ .

$y + 1 = - 108 y - 54 \cdot 2$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Multiply $- 54$ by $2$ .

$y + 1 = - 108 y - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y + 1 = - 108 y - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y + 1 = - 108 y - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y + 1 = - 108 y - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y + 1 = - 108 y - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Solve for $y$ .

Move all terms containing $y$ to the left side of the equation.

Add $108 y$ to both sides of the equation.

$y + 1 + 108 y = - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Add $y$ and $108 y$ .

$109 y + 1 = - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$109 y + 1 = - 108$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

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

Subtract $1$ from both sides of the equation.

$109 y = - 108 - 1$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Subtract $1$ from $- 108$ .

$109 y = - 109$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$109 y = - 109$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Divide each term in $109 y = - 109$ by $109$ and simplify.

Divide each term in $109 y = - 109$ by $109$ .

$\frac{109 y}{109} = \frac{- 109}{109}$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $109$ .

Cancel the common factor.

$\frac{109 y}{109} = \frac{- 109}{109}$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Divide $y$ by $1$ .

$y = \frac{- 109}{109}$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y = \frac{- 109}{109}$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y = \frac{- 109}{109}$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the right side.

Divide $- 109$ by $109$ .

$y = - 1$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y = - 1$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y = - 1$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y = - 1$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$y = - 1$

$z = \frac{3 (9 y + 11)}{2}$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $z = \frac{3 (9 y + 11)}{2}$ with $- 1$ .

$z = \frac{3 (9 (- 1) + 11)}{2}$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the right side.

Simplify $\frac{3 (9 (- 1) + 11)}{2}$ .

Simplify the numerator.

Multiply $9$ by $- 1$ .

$z = \frac{3 (- 9 + 11)}{2}$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Add $- 9$ and $11$ .

$z = \frac{3 \cdot 2}{2}$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = \frac{3 \cdot 2}{2}$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Simplify the expression.

Multiply $3$ by $2$ .

$z = \frac{6}{2}$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

Divide $6$ by $2$ .

$z = 3$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 3$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 3$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

$z = 3$

$y = - 1$

$x = - \frac{5 y}{2} - \frac{1}{2}$

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

$x = - \frac{5 (- 1)}{2} - \frac{1}{2}$

$z = 3$

$y = - 1$

Simplify the right side.

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

Combine the numerators over the common denominator.

$x = \frac{- 5 \cdot - 1 - 1}{2}$

$z = 3$

$y = - 1$

Simplify the expression.

Multiply $- 5$ by $- 1$ .

$x = \frac{5 - 1}{2}$

$z = 3$

$y = - 1$

Subtract $1$ from $5$ .

$x = \frac{4}{2}$

$z = 3$

$y = - 1$

Divide $4$ by $2$ .

$x = 2$

$z = 3$

$y = - 1$

$x = 2$

$z = 3$

$y = - 1$

$x = 2$

$z = 3$

$y = - 1$

$x = 2$

$z = 3$

$y = - 1$

$x = 2$

$z = 3$

$y = - 1$

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

$(2, - 1, 3)$

The result can be shown in multiple forms.

Point Form:

$(2, - 1, 3)$

Equation Form:

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

Solve the System of Equations -x-2y=-4z+12 3x-6y+z=15 2x+5y+1=0

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