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

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

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.

$$y+z+2y+3z=0 y+z+y+z=0$$

Solve these equations for y and z respectively.

$$y=-\frac{4}{3}z z=-y$$

Substitute -\frac{4}{3}z for y in the equation z=-y.

$$z=-\left(-\frac{4}{3}\right)z$$

Solve z=-\left(-\frac{4}{3}\right)z for z.

$$z=0$$

Substitute 0 for z in the equation y=-\frac{4}{3}z.

$$y=-\frac{4}{3}\times 0$$

Calculate y from y=-\frac{4}{3}\times 0.

$$y=0$$

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.

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