Solve {l}{7x-5y=2}{z=5y+7y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 7 x - 5 y = 2 }\\ { z = 5 y + 7 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{5a}{84}+\frac{2}{7}$$

$$y=\frac{a}{12}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=5y+7y 7x-5y=2 a=z$$

Calculate z from z=5y+7y.

$$z=12y$$

Substitute 12y for z in the equation a=z.

$$a=12y$$

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

$$x=\frac{5}{7}y+\frac{2}{7} y=\frac{1}{12}a$$

Substitute \frac{1}{12}a for y in the equation x=\frac{5}{7}y+\frac{2}{7}.

$$x=\frac{5}{7}\times \frac{1}{12}a+\frac{2}{7}$$

Calculate x from x=\frac{5}{7}\times \frac{1}{12}a+\frac{2}{7}.

$$x=\frac{2}{7}+\frac{5}{84}a$$

Substitute \frac{1}{12}a for y in the equation z=12y.

$$z=12\times \frac{1}{12}a$$

Calculate z from z=12\times \frac{1}{12}a.

$$z=a$$

The system is now solved.

$$x=\frac{2}{7}+\frac{5}{84}a y=\frac{1}{12}a z=a$$