Solve {c}{2x+2y+z=-2}{-x-2y+2z=-5}{2x+4y+z=0}

$$\left. \begin{array} { c } { 2 x + 2 y + z = - 2 } \\ { - x - 2 y + 2 z = - 5 } \\ { 2 x + 4 y + z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=1$$

$$z=-2$$

Short Steps Using Substitution

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

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

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

$$-x-2y+2\left(-2-2x-2y\right)=-5 2x+4y-2-2x-2y=0$$

Solve these equations for x and y respectively.

$$x=-\frac{6}{5}y+\frac{1}{5} y=1$$

Substitute 1 for y in the equation x=-\frac{6}{5}y+\frac{1}{5}.

$$x=-\frac{6}{5}+\frac{1}{5}$$

Calculate x from x=-\frac{6}{5}+\frac{1}{5}.

$$x=-1$$

Substitute -1 for x and 1 for y in the equation z=-2-2x-2y.

$$z=-2-2\left(-1\right)-2$$

Calculate z from z=-2-2\left(-1\right)-2.

$$z=-2$$

The system is now solved.

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