Solve {c}{x+y+z=0}{2x-y+2z=0}{-3x+2y+3z=0}

$$\left. \begin{array} { c } { x + y + z = 0 } \\ { 2 x - y + 2 z = 0 } \\ { - 3 x + 2 y + 3 z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve x+y+z=0 for x.

$$x=-y-z$$

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

$$2\left(-y-z\right)-y+2z=0 -3\left(-y-z\right)+2y+3z=0$$

Solve these equations for y and z respectively.

$$y=0 z=-\frac{5}{6}y$$

Substitute 0 for y in the equation z=-\frac{5}{6}y.

$$z=-\frac{5}{6}\times 0$$

Calculate z from z=-\frac{5}{6}\times 0.

$$z=0$$

Substitute 0 for y and 0 for z in the equation x=-y-z.

$$x=-0-0$$

Calculate x from x=-0-0.

$$x=0$$

The system is now solved.

$$x=0 y=0 z=0$$