Solve {l}{2x-3y-4z=60}{3x+6y+9z=-156}{4x+8y-6z=-64}

$$\left. \begin{array} { l } { 2 x - 3 y - 4 z = 60 } \\ { 3 x + 6 y + 9 z = - 156 } \\ { 4 x + 8 y - 6 z = - 64 } \end{array} \right.$$

Solve for x, y, z

$$x=-4$$

$$y=-12$$

$$z=-8$$

Short Steps Using Substitution

Solve 2x-3y-4z=60 for x.

$$x=\frac{3}{2}y+2z+30$$

Substitute \frac{3}{2}y+2z+30 for x in the second and third equation.

$$3\left(\frac{3}{2}y+2z+30\right)+6y+9z=-156 4\left(\frac{3}{2}y+2z+30\right)+8y-6z=-64$$

Solve these equations for y and z respectively.

$$y=-\frac{164}{7}-\frac{10}{7}z z=-92-7y$$

Substitute -\frac{164}{7}-\frac{10}{7}z for y in the equation z=-92-7y.

$$z=-92-7\left(-\frac{164}{7}-\frac{10}{7}z\right)$$

Solve z=-92-7\left(-\frac{164}{7}-\frac{10}{7}z\right) for z.

$$z=-8$$

Substitute -8 for z in the equation y=-\frac{164}{7}-\frac{10}{7}z.

$$y=-\frac{164}{7}-\frac{10}{7}\left(-8\right)$$

Calculate y from y=-\frac{164}{7}-\frac{10}{7}\left(-8\right).

$$y=-12$$

Substitute -12 for y and -8 for z in the equation x=\frac{3}{2}y+2z+30.

$$x=\frac{3}{2}\left(-12\right)+2\left(-8\right)+30$$

Calculate x from x=\frac{3}{2}\left(-12\right)+2\left(-8\right)+30.

$$x=-4$$

The system is now solved.

$$x=-4 y=-12 z=-8$$