Solve the System of Equations -2z=6 3y+4z=-6 -2x+5y+5z=-9

$- 2 z = 6$ $3 y + 4 z = - 6$ $- 2 x + 5 y + 5 z = - 9$

Divide each term in $- 2 z = 6$ by $- 2$ and simplify.

Divide each term in $- 2 z = 6$ by $- 2$ .

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

$3 y + 4 z = - 6$

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$3 y + 4 z = - 6$

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

Divide $z$ by $1$ .

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

$3 y + 4 z = - 6$

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

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

$3 y + 4 z = - 6$

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

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

$3 y + 4 z = - 6$

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

Simplify the right side.

Divide $6$ by $- 2$ .

$z = - 3$

$3 y + 4 z = - 6$

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

$z = - 3$

$3 y + 4 z = - 6$

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

$z = - 3$

$3 y + 4 z = - 6$

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

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

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

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

$z = - 3$

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

Simplify the left side.

Multiply $4$ by $- 3$ .

$3 y - 12 = - 6$

$z = - 3$

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

$3 y - 12 = - 6$

$z = - 3$

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

Replace all occurrences of $z$ in $- 2 x + 5 y + 5 z = - 9$ with $- 3$ .

$- 2 x + 5 y + 5 (- 3) = - 9$

$3 y - 12 = - 6$

$z = - 3$

Simplify the left side.

Multiply $5$ by $- 3$ .

$- 2 x + 5 y - 15 = - 9$

$3 y - 12 = - 6$

$z = - 3$

$- 2 x + 5 y - 15 = - 9$

$3 y - 12 = - 6$

$z = - 3$

$- 2 x + 5 y - 15 = - 9$

$3 y - 12 = - 6$

$z = - 3$

Solve for $y$ in $3 y - 12 = - 6$ .

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

Add $12$ to both sides of the equation.

$3 y = - 6 + 12$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

Add $- 6$ and $12$ .

$3 y = 6$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

$3 y = 6$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

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

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

Divide $y$ by $1$ .

$y = \frac{6}{3}$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

$y = \frac{6}{3}$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

$y = \frac{6}{3}$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

Simplify the right side.

Divide $6$ by $3$ .

$y = 2$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

$y = 2$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

$y = 2$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

$y = 2$

$- 2 x + 5 y - 15 = - 9$

$z = - 3$

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

Replace all occurrences of $y$ in $- 2 x + 5 y - 15 = - 9$ with $2$ .

$- 2 x + 5 (2) - 15 = - 9$

$y = 2$

$z = - 3$

Simplify the left side.

Simplify $- 2 x + 5 (2) - 15$ .

Multiply $5$ by $2$ .

$- 2 x + 10 - 15 = - 9$

$y = 2$

$z = - 3$

Subtract $15$ from $10$ .

$- 2 x - 5 = - 9$

$y = 2$

$z = - 3$

$- 2 x - 5 = - 9$

$y = 2$

$z = - 3$

$- 2 x - 5 = - 9$

$y = 2$

$z = - 3$

$- 2 x - 5 = - 9$

$y = 2$

$z = - 3$

Solve for $x$ in $- 2 x - 5 = - 9$ .

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

Add $5$ to both sides of the equation.

$- 2 x = - 9 + 5$

$y = 2$

$z = - 3$

Add $- 9$ and $5$ .

$- 2 x = - 4$

$y = 2$

$z = - 3$

$- 2 x = - 4$

$y = 2$

$z = - 3$

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

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

$y = 2$

$z = - 3$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$y = 2$

$z = - 3$

Divide $x$ by $1$ .

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

$y = 2$

$z = - 3$

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

$y = 2$

$z = - 3$

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

$y = 2$

$z = - 3$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

$y = 2$

$z = - 3$

$x = 2$

$y = 2$

$z = - 3$

$x = 2$

$y = 2$

$z = - 3$

$x = 2$

$y = 2$

$z = - 3$

Solve the system of equations $x = 2 y = 2 z = - 3$ .

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

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

$(2, 2, - 3)$

The result can be shown in multiple forms.

Point Form:

$(2, 2, - 3)$

Equation Form:

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

Solve the System of Equations -2z=6 3y+4z=-6 -2x+5y+5z=-9

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