Solve {l}{y=3/4x-2}{z={(3)}x+2}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = \frac{3}{4} x - 2 }\\ { z = {(3)} x + 2 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a-2}{3}$$

$$y=\frac{a-10}{4}$$

$$z=a$$

Short Steps Using Substitution

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

$$x=-\frac{2}{3}+\frac{1}{3}z z=a$$

Substitute a for z in the equation x=-\frac{2}{3}+\frac{1}{3}z.

$$x=-\frac{2}{3}+\frac{1}{3}a$$

Substitute -\frac{2}{3}+\frac{1}{3}a for x in the equation y=\frac{3}{4}x-2.

$$y=\frac{3}{4}\left(-\frac{2}{3}+\frac{1}{3}a\right)-2$$

Calculate y from y=\frac{3}{4}\left(-\frac{2}{3}+\frac{1}{3}a\right)-2.

$$y=-\frac{5}{2}+\frac{1}{4}a$$

The system is now solved.

$$x=-\frac{2}{3}+\frac{1}{3}a y=-\frac{5}{2}+\frac{1}{4}a z=a$$