Solve {l}{3x+2y-z=7}{6x-3y=-2}{3y-2z=8}

$$\left\{ \begin{array} { l } { 3 x + 2 y - z = 7 } \\ { 6 x - 3 y = - 2 } \\ { 3 y - 2 z = 8 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{2}{3}\approx 0.666666667$$

$$y=2$$

$$z=-1$$

Short Steps Using Substitution

Solve 3x+2y-z=7 for z.

$$z=3x+2y-7$$

Substitute 3x+2y-7 for z in the equation 3y-2z=8.

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

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

$$y=\frac{2}{3}+2x x=1-\frac{1}{6}y$$

Substitute \frac{2}{3}+2x for y in the equation x=1-\frac{1}{6}y.

$$x=1-\frac{1}{6}\left(\frac{2}{3}+2x\right)$$

Solve x=1-\frac{1}{6}\left(\frac{2}{3}+2x\right) for x.

$$x=\frac{2}{3}$$

Substitute \frac{2}{3} for x in the equation y=\frac{2}{3}+2x.

$$y=\frac{2}{3}+2\times \frac{2}{3}$$

Calculate y from y=\frac{2}{3}+2\times \frac{2}{3}.

$$y=2$$

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

$$z=3\times \frac{2}{3}+2\times 2-7$$

Calculate z from z=3\times \frac{2}{3}+2\times 2-7.

$$z=-1$$

The system is now solved.

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