Solve {l}{12/y+frac{4{5}}=1/5}{z=y+4}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { \frac{12}{y + \frac{4}{5}} = \frac{1}{5} }\\ { z = y + 4 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, z, a

$$a = \frac{316}{5} = 63\frac{1}{5} = 63.2$$

Short Steps Using Substitution

Reorder the equations.

$$z=y+4 \frac{12}{y+\frac{4}{5}}=\frac{1}{5} a=z$$

Substitute y+4 for z in the equation a=z.

$$a=y+4$$

Solve \frac{12}{y+\frac{4}{5}}=\frac{1}{5} for y.

$$y=\frac{296}{5}$$

Substitute \frac{296}{5} for y in the equation a=y+4.

$$a=\frac{296}{5}+4$$

Calculate a from a=\frac{296}{5}+4.

$$a=\frac{316}{5}$$

Substitute \frac{296}{5} for y in the equation z=y+4.

$$z=\frac{296}{5}+4$$

Calculate z from z=\frac{296}{5}+4.

$$z=\frac{316}{5}$$

The system is now solved.

$$y=\frac{296}{5} z=\frac{316}{5} a=\frac{316}{5}$$