Solve {l}{8y+2z=-7}{3x+5y+2z=8}{6x+2y+8z=26}

$$\left. \begin{array} { l } { 8 y + 2 z = - 7 } \\ { 3 x + 5 y + 2 z = 8 } \\ { 6 x + 2 y + 8 z = 26 } \end{array} \right.$$

Solve for y, z, x

$$x=4$$

$$y=-1$$

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

Short Steps Using Substitution

Solve 8y+2z=-7 for y.

$$y=-\frac{1}{4}z-\frac{7}{8}$$

Substitute -\frac{1}{4}z-\frac{7}{8} for y in the second and third equation.

$$3x+5\left(-\frac{1}{4}z-\frac{7}{8}\right)+2z=8 6x+2\left(-\frac{1}{4}z-\frac{7}{8}\right)+8z=26$$

Solve these equations for z and x respectively.

$$z=\frac{33}{2}-4x x=\frac{37}{8}-\frac{5}{4}z$$

Substitute \frac{33}{2}-4x for z in the equation x=\frac{37}{8}-\frac{5}{4}z.

$$x=\frac{37}{8}-\frac{5}{4}\left(\frac{33}{2}-4x\right)$$

Solve x=\frac{37}{8}-\frac{5}{4}\left(\frac{33}{2}-4x\right) for x.

$$x=4$$

Substitute 4 for x in the equation z=\frac{33}{2}-4x.

$$z=\frac{33}{2}-4\times 4$$

Calculate z from z=\frac{33}{2}-4\times 4.

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

Substitute \frac{1}{2} for z in the equation y=-\frac{1}{4}z-\frac{7}{8}.

$$y=-\frac{1}{4}\times \frac{1}{2}-\frac{7}{8}$$

Calculate y from y=-\frac{1}{4}\times \frac{1}{2}-\frac{7}{8}.

$$y=-1$$

The system is now solved.

$$y=-1 z=\frac{1}{2} x=4$$