Solve {l}{x+y+z=-2}{x-y+z=20}{11x+6y=0}

$$\left\{ \begin{array} { l } { x + y + z = - 2 } \\ { x - y + z = 20 } \\ { 11 x + 6 y = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=6$$

$$y=-11$$

$$z=3$$

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.

$$-y-z-2-y+z=20 11\left(-y-z-2\right)+6y=0$$

Solve these equations for y and z respectively.

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

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

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

Calculate z from z=-2-\frac{5}{11}\left(-11\right).

$$z=3$$

Substitute -11 for y and 3 for z in the equation x=-y-z-2.

$$x=-\left(-11\right)-3-2$$

Calculate x from x=-\left(-11\right)-3-2.

$$x=6$$

The system is now solved.

$$x=6 y=-11 z=3$$