Solve {l}{y=34-5/2x}{z={(5)}x+5}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = 34 - \frac{5}{2} x }\\ { z = {(5)} x + 5 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

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

$$y=\frac{73-a}{2}$$

$$z=a$$

Short Steps Using Substitution

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

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

Substitute a for z in the equation x=\frac{1}{5}z-1.

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

Substitute -1+\frac{1}{5}a for x in the equation y=34-\frac{5}{2}x.

$$y=34-\frac{5}{2}\left(-1+\frac{1}{5}a\right)$$

Calculate y from y=34-\frac{5}{2}\left(-1+\frac{1}{5}a\right).

$$y=\frac{73}{2}-\frac{1}{2}a$$

The system is now solved.

$$x=\frac{1}{5}a-1 y=\frac{73}{2}-\frac{1}{2}a z=a$$