Solve {r}{-2x+2y+5z=-3}{3y+5z=-3}{-3z=-9}

$$\left\{ \begin{array} { r } { - 2 x + 2 y + 5 z = - 3 } \\ { 3 y + 5 z = - 3 } \\ { - 3 z = - 9 } \end{array} \right.$$

Solve for x, y, z

$$x=3$$

$$y=-6$$

$$z=3$$

Solution Steps

Consider the third equation. Divide both sides by -3.

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

Divide -9 by -3 to get 3.

$$z=3$$

Consider the second equation. Insert the known values of variables into the equation.

$$3y+5\times 3=-3$$

Multiply 5 and 3 to get 15.

$$3y+15=-3$$

Subtract 15 from both sides.

$$3y=-3-15$$

Subtract 15 from -3 to get -18.

$$3y=-18$$

Divide both sides by 3.

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

Divide -18 by 3 to get -6.

$$y=-6$$

Consider the first equation. Insert the known values of variables into the equation.

$$-2x+2\left(-6\right)+5\times 3=-3$$

Do the multiplications.

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

Add -12 and 15 to get 3.

$$-2x+3=-3$$

Subtract 3 from both sides.

$$-2x=-3-3$$

Subtract 3 from -3 to get -6.

$$-2x=-6$$

Divide both sides by -2.

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

Divide -6 by -2 to get 3.

$$x=3$$

The system is now solved.

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