Solve {l}{x+y+z=2}{2x-y+z=-3}{-x+3y-z=10}

$$\left. \begin{array}{l}{ x + y + z = 2 }\\{ 2 x - y + z = - 3 }\\{ - x + 3 y - z = 10 }\end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=3$$

$$z=-2$$

Short Steps Using Substitution

Solve x+y+z=2 for x.

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

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

$$2\left(-y-z+2\right)-y+z=-3 -\left(-y-z+2\right)+3y-z=10$$

Solve these equations for z and y respectively.

$$z=-3y+7 y=3$$

Substitute 3 for y in the equation z=-3y+7.

$$z=-3\times 3+7$$

Calculate z from z=-3\times 3+7.

$$z=-2$$

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

$$x=-3-\left(-2\right)+2$$

Calculate x from x=-3-\left(-2\right)+2.

$$x=1$$

The system is now solved.

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