Solve {l}{8x+2y=46}{z=7x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 8 x + 2 y = 46 }\\ { z = 7 x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a}{7}$$

$$y=-\frac{4a}{7}+23$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=7x 8x+2y=46 a=z$$

Substitute 7x for z in the equation a=z.

$$a=7x$$

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

$$y=23-4x x=\frac{1}{7}a$$

Substitute \frac{1}{7}a for x in the equation y=23-4x.

$$y=23-4\times \frac{1}{7}a$$

Calculate y from y=23-4\times \frac{1}{7}a.

$$y=23-\frac{4}{7}a$$

Substitute \frac{1}{7}a for x in the equation z=7x.

$$z=7\times \frac{1}{7}a$$

Calculate z from z=7\times \frac{1}{7}a.

$$z=a$$

The system is now solved.

$$x=\frac{1}{7}a y=23-\frac{4}{7}a z=a$$