Solve {l}{3x+2y=3}{z=5x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 3 x + 2 y = 3 }\\ { z = 5 x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

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

$$y=-\frac{3a}{10}+\frac{3}{2}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=5x 3x+2y=3 a=z$$

Substitute 5x for z in the equation a=z.

$$a=5x$$

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

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

Substitute \frac{1}{5}a for x in the equation y=\frac{3}{2}-\frac{3}{2}x.

$$y=\frac{3}{2}-\frac{3}{2}\times \frac{1}{5}a$$

Calculate y from y=\frac{3}{2}-\frac{3}{2}\times \frac{1}{5}a.

$$y=\frac{3}{2}-\frac{3}{10}a$$

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

$$z=5\times \frac{1}{5}a$$

Calculate z from z=5\times \frac{1}{5}a.

$$z=a$$

The system is now solved.

$$x=\frac{1}{5}a y=\frac{3}{2}-\frac{3}{10}a z=a$$