Solve {c}{-4x+4y-2z=-2}{-5x-3y+2z=15}{-x+8y+2z=-48}

$$\left. \begin{array} { c } { - 4 x + 4 y - 2 z = - 2 } \\ { - 5 x - 3 y + 2 z = 15 } \\ { - x + 8 y + 2 z = - 48 } \end{array} \right.$$

Solve for x, y, z

$$x=-2$$

$$y=-5$$

$$z=-5$$

Short Steps Using Substitution

Reorder the equations.

$$-x+8y+2z=-48 -5x-3y+2z=15 -4x+4y-2z=-2$$

Solve -x+8y+2z=-48 for x.

$$x=48+8y+2z$$

Substitute 48+8y+2z for x in the second and third equation.

$$-5\left(48+8y+2z\right)-3y+2z=15 -4\left(48+8y+2z\right)+4y-2z=-2$$

Solve these equations for y and z respectively.

$$y=-\frac{255}{43}-\frac{8}{43}z z=-19-\frac{14}{5}y$$

Substitute -\frac{255}{43}-\frac{8}{43}z for y in the equation z=-19-\frac{14}{5}y.

$$z=-19-\frac{14}{5}\left(-\frac{255}{43}-\frac{8}{43}z\right)$$

Solve z=-19-\frac{14}{5}\left(-\frac{255}{43}-\frac{8}{43}z\right) for z.

$$z=-5$$

Substitute -5 for z in the equation y=-\frac{255}{43}-\frac{8}{43}z.

$$y=-\frac{255}{43}-\frac{8}{43}\left(-5\right)$$

Calculate y from y=-\frac{255}{43}-\frac{8}{43}\left(-5\right).

$$y=-5$$

Substitute -5 for y and -5 for z in the equation x=48+8y+2z.

$$x=48+8\left(-5\right)+2\left(-5\right)$$

Calculate x from x=48+8\left(-5\right)+2\left(-5\right).

$$x=-2$$

The system is now solved.

$$x=-2 y=-5 z=-5$$