Solve {l}{8x-2y-4=0}{z=1-2y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 8 x - 2 y - 4 = 0 }\\ { z = 1 - 2 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{5-a}{8}$$

$$y=\frac{1-a}{2}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=1-2y 8x-2y-4=0 a=z$$

Substitute 1-2y for z in the equation a=z.

$$a=1-2y$$

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

$$x=\frac{1}{2}+\frac{1}{4}y y=\frac{1}{2}-\frac{1}{2}a$$

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

$$x=\frac{1}{2}+\frac{1}{4}\left(\frac{1}{2}-\frac{1}{2}a\right)$$

Calculate x from x=\frac{1}{2}+\frac{1}{4}\left(\frac{1}{2}-\frac{1}{2}a\right).

$$x=\frac{5}{8}-\frac{1}{8}a$$

Substitute \frac{1}{2}-\frac{1}{2}a for y in the equation z=1-2y.

$$z=1-2\left(\frac{1}{2}-\frac{1}{2}a\right)$$

Calculate z from z=1-2\left(\frac{1}{2}-\frac{1}{2}a\right).

$$z=a$$

The system is now solved.

$$x=\frac{5}{8}-\frac{1}{8}a y=\frac{1}{2}-\frac{1}{2}a z=a$$