Solve {l}{x+y+z=2z}{z=2x}{y=1/3x}

$$\left\{ \begin{array} { l } { x + y + z = 2 z } \\ { z = 2 x } \\ { y = \frac { 1 } { 3 } x } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Reorder the equations.

$$z=2x x+y+z=2z y=\frac{1}{3}x$$

Substitute 2x for z in the equation x+y+z=2z.

$$x+y+2x=2\times 2x$$

Solve the second equation for y and the third equation for x.

$$y=x x=3y$$

Substitute x for y in the equation x=3y.

$$x=3x$$

Solve x=3x for x.

$$x=0$$

Substitute 0 for x in the equation y=x.

$$y=0$$

Substitute 0 for x in the equation z=2x.

$$z=2\times 0$$

Calculate z from z=2\times 0.

$$z=0$$

The system is now solved.

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