Solve {l}{x=2y}{z=5-y}{m=x+z}

$$\left. \begin{array} { l } { x = 2 y } \\ { z = 5 - y } \\ { m = x + z } \end{array} \right.$$

Solve for x, y, z

$$x=2\left(m-5\right)$$

$$y=m-5$$

$$z=10-m$$

Short Steps Using Substitution

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

$$m=2y+z$$

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

$$y=-z+5 z=m-2y$$

Substitute -z+5 for y in the equation z=m-2y.

$$z=m-2\left(-z+5\right)$$

Solve z=m-2\left(-z+5\right) for z.

$$z=10-m$$

Substitute 10-m for z in the equation y=-z+5.

$$y=-\left(10-m\right)+5$$

Calculate y from y=-\left(10-m\right)+5.

$$y=-5+m$$

Substitute -5+m for y in the equation x=2y.

$$x=2\left(-5+m\right)$$

Calculate x from x=2\left(-5+m\right).

$$x=-10+2m$$

The system is now solved.

$$x=-10+2m y=-5+m z=10-m$$