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

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

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve x+y=0 for x.

$$x=-y$$

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

$$2\left(-1\right)y-2y+z=0 4\left(-1\right)y-2z=0$$

Solve these equations for y and z respectively.

$$y=\frac{1}{4}z z=-2y$$

Substitute \frac{1}{4}z for y in the equation z=-2y.

$$z=-2\times \frac{1}{4}z$$

Solve z=-2\times \frac{1}{4}z for z.

$$z=0$$

Substitute 0 for z in the equation y=\frac{1}{4}z.

$$y=\frac{1}{4}\times 0$$

Calculate y from y=\frac{1}{4}\times 0.

$$y=0$$

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

$$x=-0$$

Calculate x from x=-0.

$$x=0$$

The system is now solved.

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