Solve {l}{2x+y-z=-8}{-x+y+z=3}{-2x+4z=18}

$$\left\{ \begin{array}{l}{ 2 x + y - z = - 8 }\\{ - x + y + z = 3 }\\{ - 2 x + 4 z = 18 }\end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=-2$$

$$z=4$$

Short Steps Using Substitution

Solve 2x+y-z=-8 for y.

$$y=-2x+z-8$$

Substitute -2x+z-8 for y in the equation -x+y+z=3.

$$-x-2x+z-8+z=3$$

Solve the second equation for x and the third equation for z.

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

Substitute \frac{2}{3}z-\frac{11}{3} for x in the equation z=\frac{9}{2}+\frac{1}{2}x.

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

Solve z=\frac{9}{2}+\frac{1}{2}\left(\frac{2}{3}z-\frac{11}{3}\right) for z.

$$z=4$$

Substitute 4 for z in the equation x=\frac{2}{3}z-\frac{11}{3}.

$$x=\frac{2}{3}\times 4-\frac{11}{3}$$

Calculate x from x=\frac{2}{3}\times 4-\frac{11}{3}.

$$x=-1$$

Substitute -1 for x and 4 for z in the equation y=-2x+z-8.

$$y=-2\left(-1\right)+4-8$$

Calculate y from y=-2\left(-1\right)+4-8.

$$y=-2$$

The system is now solved.

$$x=-1 y=-2 z=4$$