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

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

Solve for x, y, z

$$x=\frac{a}{2}$$

$$y=\frac{a-16}{4}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

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

Substitute 2x for z in the equation a=z.

$$a=2x$$

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

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

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

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

Calculate y from y=\frac{1}{2}\times \frac{1}{2}a-4.

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

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

$$z=2\times \frac{1}{2}a$$

Calculate z from z=2\times \frac{1}{2}a.

$$z=a$$

The system is now solved.

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