Solve {c}{2x+2y-z=-7}{x+2y-3z=-8}{4x-2y+z=-11}

$$\left\{ \begin{array} { c } { 2 x + 2 y - z = - 7 } \\ { x + 2 y - 3 z = - 8 } \\ { 4 x - 2 y + z = - 11 } \end{array} \right.$$

Solve for x, y, z

$$x=-3$$

$$y=\frac{1}{2}=0.5$$

$$z=2$$

Short Steps Using Substitution

Solve 2x+2y-z=-7 for z.

$$z=2x+2y+7$$

Substitute 2x+2y+7 for z in the second and third equation.

$$x+2y-3\left(2x+2y+7\right)=-8 4x-2y+2x+2y+7=-11$$

Solve these equations for y and x respectively.

$$y=-\frac{13}{4}-\frac{5}{4}x x=-3$$

Substitute -3 for x in the equation y=-\frac{13}{4}-\frac{5}{4}x.

$$y=-\frac{13}{4}-\frac{5}{4}\left(-3\right)$$

Calculate y from y=-\frac{13}{4}-\frac{5}{4}\left(-3\right).

$$y=\frac{1}{2}$$

Substitute \frac{1}{2} for y and -3 for x in the equation z=2x+2y+7.

$$z=2\left(-3\right)+2\times \frac{1}{2}+7$$

Calculate z from z=2\left(-3\right)+2\times \frac{1}{2}+7.

$$z=2$$

The system is now solved.

$$x=-3 y=\frac{1}{2} z=2$$