Solve {l}{x+3z=21}{9y-z=-86}{5x+7y=-33}

$$\left\{ \begin{array} { l } { x + 3 z = 21 } \\ { 9 y - z = - 86 } \\ { 5 x + 7 y = - 33 } \end{array} \right.$$

Solve for x, z, y

$$x=6$$

$$y=-9$$

$$z=5$$

Short Steps Using Substitution

Solve x+3z=21 for x.

$$x=21-3z$$

Substitute 21-3z for x in the equation 5x+7y=-33.

$$5\left(21-3z\right)+7y=-33$$

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

$$z=9y+86 y=-\frac{138}{7}+\frac{15}{7}z$$

Substitute 9y+86 for z in the equation y=-\frac{138}{7}+\frac{15}{7}z.

$$y=-\frac{138}{7}+\frac{15}{7}\left(9y+86\right)$$

Solve y=-\frac{138}{7}+\frac{15}{7}\left(9y+86\right) for y.

$$y=-9$$

Substitute -9 for y in the equation z=9y+86.

$$z=9\left(-9\right)+86$$

Calculate z from z=9\left(-9\right)+86.

$$z=5$$

Substitute 5 for z in the equation x=21-3z.

$$x=21-3\times 5$$

Calculate x from x=21-3\times 5.

$$x=6$$

The system is now solved.

$$x=6 z=5 y=-9$$