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

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

Step 1

Divide each term in $- 3 z = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 z = - 9$ by $- 3$ .

$\frac{- 3 z}{- 3} = \frac{- 9}{- 3}$

$3 y + 5 z = - 3$

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 z}{- 3} = \frac{- 9}{- 3}$

$3 y + 5 z = - 3$

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

Divide $z$ by $1$ .

$z = \frac{- 9}{- 3}$

$3 y + 5 z = - 3$

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

$z = \frac{- 9}{- 3}$

$3 y + 5 z = - 3$

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

$z = \frac{- 9}{- 3}$

$3 y + 5 z = - 3$

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

Simplify the right side.

Divide $- 9$ by $- 3$ .

$z = 3$

$3 y + 5 z = - 3$

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

$z = 3$

$3 y + 5 z = - 3$

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

$z = 3$

$3 y + 5 z = - 3$

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

Step 2

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

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

$3 y + 5 (3) = - 3$

$z = 3$

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

Simplify the left side.

Multiply $5$ by $3$ .

$3 y + 15 = - 3$

$z = 3$

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

$3 y + 15 = - 3$

$z = 3$

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

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

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

$3 y + 15 = - 3$

$z = 3$

Simplify the left side.

Multiply $5$ by $3$ .

$- 2 x + 2 y + 15 = - 3$

$3 y + 15 = - 3$

$z = 3$

$- 2 x + 2 y + 15 = - 3$

$3 y + 15 = - 3$

$z = 3$

$- 2 x + 2 y + 15 = - 3$

$3 y + 15 = - 3$

$z = 3$

Step 3

Solve for $y$ in $3 y + 15 = - 3$ .

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

Subtract $15$ from both sides of the equation.

$3 y = - 3 - 15$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

Subtract $15$ from $- 3$ .

$3 y = - 18$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

$3 y = - 18$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

Divide each term in $3 y = - 18$ by $3$ and simplify.

Divide each term in $3 y = - 18$ by $3$ .

$\frac{3 y}{3} = \frac{- 18}{3}$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 18}{3}$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

Divide $y$ by $1$ .

$y = \frac{- 18}{3}$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

$y = \frac{- 18}{3}$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

$y = \frac{- 18}{3}$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

Simplify the right side.

Divide $- 18$ by $3$ .

$y = - 6$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

$y = - 6$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

$y = - 6$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

$y = - 6$

$- 2 x + 2 y + 15 = - 3$

$z = 3$

Step 4

Replace all occurrences of $y$ with $- 6$ in each equation.

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

$- 2 x + 2 (- 6) + 15 = - 3$

$y = - 6$

$z = 3$

Simplify the left side.

Simplify $- 2 x + 2 (- 6) + 15$ .

Multiply $2$ by $- 6$ .

$- 2 x - 12 + 15 = - 3$

$y = - 6$

$z = 3$

Add $- 12$ and $15$ .

$- 2 x + 3 = - 3$

$y = - 6$

$z = 3$

$- 2 x + 3 = - 3$

$y = - 6$

$z = 3$

$- 2 x + 3 = - 3$

$y = - 6$

$z = 3$

$- 2 x + 3 = - 3$

$y = - 6$

$z = 3$

Step 5

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

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

Subtract $3$ from both sides of the equation.

$- 2 x = - 3 - 3$

$y = - 6$

$z = 3$

Subtract $3$ from $- 3$ .

$- 2 x = - 6$

$y = - 6$

$z = 3$

$- 2 x = - 6$

$y = - 6$

$z = 3$

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

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

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

$y = - 6$

$z = 3$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$y = - 6$

$z = 3$

Divide $x$ by $1$ .

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

$y = - 6$

$z = 3$

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

$y = - 6$

$z = 3$

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

$y = - 6$

$z = 3$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$x = 3$

$y = - 6$

$z = 3$

$x = 3$

$y = - 6$

$z = 3$

$x = 3$

$y = - 6$

$z = 3$

$x = 3$

$y = - 6$

$z = 3$

Step 6

Solve the system of equations $x = 3 y = - 6 z = 3$ .

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

Step 7

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

$(3, - 6, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(3, - 6, 3)$

Equation Form:

$x = 3, y = - 6, z = 3$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.