Solve {l}{x+y=z}{4x-y=3z}{9x+6y=7z}

$$\left\{ \begin{array} { l } { x + y = z } \\ { 4 x - y = 3 z } \\ { 9 x + 6 y = 7 z } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve x+y=z for z.

$$z=x+y$$

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

$$4x-y=3\left(x+y\right) 9x+6y=7\left(x+y\right)$$

Solve these equations for y and x respectively.

$$y=\frac{1}{4}x x=\frac{1}{2}y$$

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

$$x=\frac{1}{2}\times \frac{1}{4}x$$

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

$$x=0$$

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

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

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

$$y=0$$

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

$$z=0+0$$

Calculate z from z=0+0.

$$z=0$$

The system is now solved.

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