Solve {l}{9x+8y+6z=-122}{2x+6y+9z=-95}{-8x+5y-3z=12}

$$\left. \begin{array} { l } { 9 x + 8 y + 6 z = - 122 } \\ { 2 x + 6 y + 9 z = - 95 } \\ { - 8 x + 5 y - 3 z = 12 } \end{array} \right.$$

Solve for x, y, z

$$x=-4$$

$$y=-7$$

$$z=-5$$

Short Steps Using Substitution

Solve 9x+8y+6z=-122 for x.

$$x=-\frac{122}{9}-\frac{8}{9}y-\frac{2}{3}z$$

Substitute -\frac{122}{9}-\frac{8}{9}y-\frac{2}{3}z for x in the second and third equation.

$$2\left(-\frac{122}{9}-\frac{8}{9}y-\frac{2}{3}z\right)+6y+9z=-95 -8\left(-\frac{122}{9}-\frac{8}{9}y-\frac{2}{3}z\right)+5y-3z=12$$

Solve these equations for y and z respectively.

$$y=-\frac{611}{38}-\frac{69}{38}z z=-\frac{124}{3}-\frac{109}{21}y$$

Substitute -\frac{611}{38}-\frac{69}{38}z for y in the equation z=-\frac{124}{3}-\frac{109}{21}y.

$$z=-\frac{124}{3}-\frac{109}{21}\left(-\frac{611}{38}-\frac{69}{38}z\right)$$

Solve z=-\frac{124}{3}-\frac{109}{21}\left(-\frac{611}{38}-\frac{69}{38}z\right) for z.

$$z=-5$$

Substitute -5 for z in the equation y=-\frac{611}{38}-\frac{69}{38}z.

$$y=-\frac{611}{38}-\frac{69}{38}\left(-5\right)$$

Calculate y from y=-\frac{611}{38}-\frac{69}{38}\left(-5\right).

$$y=-7$$

Substitute -7 for y and -5 for z in the equation x=-\frac{122}{9}-\frac{8}{9}y-\frac{2}{3}z.

$$x=-\frac{122}{9}-\frac{8}{9}\left(-7\right)-\frac{2}{3}\left(-5\right)$$

Calculate x from x=-\frac{122}{9}-\frac{8}{9}\left(-7\right)-\frac{2}{3}\left(-5\right).

$$x=-4$$

The system is now solved.

$$x=-4 y=-7 z=-5$$