Solve {l}{x+y+z=0}{-8x+6y=-4}{-6y-4z=-12}

$$\left. \begin{array} { l } { x + y + z = 0 } \\ { - 8 x + 6 y = - 4 } \\ { - 6 y - 4 z = - 12 } \end{array} \right.$$

Solve for x, y, z

$$x=-10$$

$$y=-14$$

$$z=24$$

Short Steps Using Substitution

Solve x+y+z=0 for x.

$$x=-y-z$$

Substitute -y-z for x in the equation -8x+6y=-4.

$$-8\left(-y-z\right)+6y=-4$$

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

$$y=-\frac{2}{7}-\frac{4}{7}z z=3-\frac{3}{2}y$$

Substitute -\frac{2}{7}-\frac{4}{7}z for y in the equation z=3-\frac{3}{2}y.

$$z=3-\frac{3}{2}\left(-\frac{2}{7}-\frac{4}{7}z\right)$$

Solve z=3-\frac{3}{2}\left(-\frac{2}{7}-\frac{4}{7}z\right) for z.

$$z=24$$

Substitute 24 for z in the equation y=-\frac{2}{7}-\frac{4}{7}z.

$$y=-\frac{2}{7}-\frac{4}{7}\times 24$$

Calculate y from y=-\frac{2}{7}-\frac{4}{7}\times 24.

$$y=-14$$

Substitute -14 for y and 24 for z in the equation x=-y-z.

$$x=-\left(-14\right)-24$$

Calculate x from x=-\left(-14\right)-24.

$$x=-10$$

The system is now solved.

$$x=-10 y=-14 z=24$$