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

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

Solve for x, y, z

$$x=1$$

$$y=2$$

$$z=3$$

Short Steps Using Substitution

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

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

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

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

Solve these equations for z and y respectively.

$$z=-5y+13 y=2$$

Substitute 2 for y in the equation z=-5y+13.

$$z=-5\times 2+13$$

Calculate z from z=-5\times 2+13.

$$z=3$$

Substitute 3 for z and 2 for y in the equation x=-2y-z+8.

$$x=-2\times 2-3+8$$

Calculate x from x=-2\times 2-3+8.

$$x=1$$

The system is now solved.

$$x=1 y=2 z=3$$