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

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

Solve for x, y, z

$$x=11$$

$$y = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$z = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Short Steps Using Substitution

Solve x-2y=8 for x.

$$x=8+2y$$

Substitute 8+2y for x in the equation x-2z=6.

$$8+2y-2z=6$$

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

$$y=-\frac{1}{3}z+\frac{7}{3} z=1+y$$

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

$$z=1-\frac{1}{3}z+\frac{7}{3}$$

Solve z=1-\frac{1}{3}z+\frac{7}{3} for z.

$$z=\frac{5}{2}$$

Substitute \frac{5}{2} for z in the equation y=-\frac{1}{3}z+\frac{7}{3}.

$$y=-\frac{1}{3}\times \frac{5}{2}+\frac{7}{3}$$

Calculate y from y=-\frac{1}{3}\times \frac{5}{2}+\frac{7}{3}.

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

Substitute \frac{3}{2} for y in the equation x=8+2y.

$$x=8+2\times \frac{3}{2}$$

Calculate x from x=8+2\times \frac{3}{2}.

$$x=11$$

The system is now solved.

$$x=11 y=\frac{3}{2} z=\frac{5}{2}$$