Solve {l}{x-y+z=-7}{4x+2y-z=5}{-2x+4y-z=33}

$$\left\{ \begin{array}{l}{ x - y + z = - 7 }\\{ 4 x + 2 y - z = 5 }\\{ - 2 x + 4 y - z = 33 }\end{array} \right.$$

Solve for x, y, z

$$x=-2$$

$$y=8$$

$$z=3$$

Short Steps Using Substitution

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

$$x=y-z-7$$

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

$$4\left(y-z-7\right)+2y-z=5 -2\left(y-z-7\right)+4y-z=33$$

Solve these equations for y and z respectively.

$$y=\frac{5}{6}z+\frac{11}{2} z=-2y+19$$

Substitute \frac{5}{6}z+\frac{11}{2} for y in the equation z=-2y+19.

$$z=-2\left(\frac{5}{6}z+\frac{11}{2}\right)+19$$

Solve z=-2\left(\frac{5}{6}z+\frac{11}{2}\right)+19 for z.

$$z=3$$

Substitute 3 for z in the equation y=\frac{5}{6}z+\frac{11}{2}.

$$y=\frac{5}{6}\times 3+\frac{11}{2}$$

Calculate y from y=\frac{5}{6}\times 3+\frac{11}{2}.

$$y=8$$

Substitute 8 for y and 3 for z in the equation x=y-z-7.

$$x=8-3-7$$

Calculate x from x=8-3-7.

$$x=-2$$

The system is now solved.

$$x=-2 y=8 z=3$$