Solve {l}{2x-y=-4}{z=y-10-x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 2 x - y = -4 }\\ { z = y - 10 - x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=a+6$$

$$y=2\left(a+8\right)$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=y-10-x 2x-y=-4 a=z$$

Substitute y-10-x for z in the equation a=z.

$$a=y-10-x$$

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

$$y=4+2x x=y-a-10$$

Substitute 4+2x for y in the equation x=y-a-10.

$$x=4+2x-a-10$$

Solve x=4+2x-a-10 for x.

$$x=6+a$$

Substitute 6+a for x in the equation y=4+2x.

$$y=4+2\left(6+a\right)$$

Calculate y from y=4+2\left(6+a\right).

$$y=16+2a$$

Substitute 16+2a for y and 6+a for x in the equation z=y-10-x.

$$z=16+2a-10-\left(6+a\right)$$

Calculate z from z=16+2a-10-\left(6+a\right).

$$z=a$$

The system is now solved.

$$x=6+a y=16+2a z=a$$