Solve {l}{-x-4y-4z=-7}{3x+4y+2z=8}{-x-2y+2z=-2}

$$\left. \begin{array} { l } { - x - 4 y - 4 z = - 7 } \\ { 3 x + 4 y + 2 z = 8 } \\ { - x - 2 y + 2 z = - 2 } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=1$$

$$z=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve -x-4y-4z=-7 for x.

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

Substitute -4y-4z+7 for x in the second and third equation.

$$3\left(-4y-4z+7\right)+4y+2z=8 -\left(-4y-4z+7\right)-2y+2z=-2$$

Solve these equations for y and z respectively.

$$y=-\frac{5}{4}z+\frac{13}{8} z=-\frac{1}{3}y+\frac{5}{6}$$

Substitute -\frac{5}{4}z+\frac{13}{8} for y in the equation z=-\frac{1}{3}y+\frac{5}{6}.

$$z=-\frac{1}{3}\left(-\frac{5}{4}z+\frac{13}{8}\right)+\frac{5}{6}$$

Solve z=-\frac{1}{3}\left(-\frac{5}{4}z+\frac{13}{8}\right)+\frac{5}{6} for z.

$$z=\frac{1}{2}$$

Substitute \frac{1}{2} for z in the equation y=-\frac{5}{4}z+\frac{13}{8}.

$$y=-\frac{5}{4}\times \frac{1}{2}+\frac{13}{8}$$

Calculate y from y=-\frac{5}{4}\times \frac{1}{2}+\frac{13}{8}.

$$y=1$$

Substitute 1 for y and \frac{1}{2} for z in the equation x=-4y-4z+7.

$$x=-4-4\times \frac{1}{2}+7$$

Calculate x from x=-4-4\times \frac{1}{2}+7.

$$x=1$$

The system is now solved.

$$x=1 y=1 z=\frac{1}{2}$$