Solve {l}{-4x-8y-2z-6w=-2}{-4y-24z-8w=-32}{-4z-4w=-8}

$$\left. \begin{array}{l}{ - 4 x - 8 y - 2 z - 6 w = - 2 }\\{ - 4 y - 24 z - 8 w = - 32 }\\{ - 4 z - 4 w = - 8 }\end{array} \right.$$

Solve for x, y, z

$$x=\frac{15}{2}-9w$$

$$y=4w-4$$

$$z=2-w$$

Short Steps Using Substitution

Solve -4x-8y-2z-6w=-2 for x.

$$x=\frac{1}{2}-2y-\frac{1}{2}z-\frac{3}{2}w$$

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

$$y=8-6z-2w z=-w+2$$

Substitute -w+2 for z in the equation y=8-6z-2w.

$$y=8-6\left(-w+2\right)-2w$$

Calculate y from y=8-6\left(-w+2\right)-2w.

$$y=-4+4w$$

Substitute -4+4w for y and -w+2 for z in the equation x=\frac{1}{2}-2y-\frac{1}{2}z-\frac{3}{2}w.

$$x=\frac{1}{2}-2\left(-4+4w\right)-\frac{1}{2}\left(-w+2\right)-\frac{3}{2}w$$

Calculate x from x=\frac{1}{2}-2\left(-4+4w\right)-\frac{1}{2}\left(-w+2\right)-\frac{3}{2}w.

$$x=\frac{15}{2}-9w$$

The system is now solved.

$$x=\frac{15}{2}-9w y=-4+4w z=-w+2$$