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

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

Solve for x, z, y

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$y = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

$$z=-\frac{2}{3}\approx -0.666666667$$

Short Steps Using Substitution

Solve x+x+z=2 for z.

$$z=2-2x$$

Substitute 2-2x for z in the second and third equation.

$$x-y+2-2x=-2 x-\left(2-2x\right)=y+2-2x$$

Solve these equations for x and y respectively.

$$x=-y+4 y=-4+5x$$

Substitute -y+4 for x in the equation y=-4+5x.

$$y=-4+5\left(-y+4\right)$$

Solve y=-4+5\left(-y+4\right) for y.

$$y=\frac{8}{3}$$

Substitute \frac{8}{3} for y in the equation x=-y+4.

$$x=-\frac{8}{3}+4$$

Calculate x from x=-\frac{8}{3}+4.

$$x=\frac{4}{3}$$

Substitute \frac{4}{3} for x in the equation z=2-2x.

$$z=2-2\times \frac{4}{3}$$

Calculate z from z=2-2\times \frac{4}{3}.

$$z=-\frac{2}{3}$$

The system is now solved.

$$x=\frac{4}{3} z=-\frac{2}{3} y=\frac{8}{3}$$