Solve {l}{6x+7y=18}{z=x+13}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 6 x + 7 y = 18 }\\ { z = x + 13 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=a-13$$

$$y=\frac{96-6a}{7}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=x+13 6x+7y=18 a=z$$

Substitute x+13 for z in the equation a=z.

$$a=x+13$$

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

$$y=\frac{18}{7}-\frac{6}{7}x x=a-13$$

Substitute a-13 for x in the equation y=\frac{18}{7}-\frac{6}{7}x.

$$y=\frac{18}{7}-\frac{6}{7}\left(a-13\right)$$

Calculate y from y=\frac{18}{7}-\frac{6}{7}\left(a-13\right).

$$y=\frac{96}{7}-\frac{6}{7}a$$

Substitute a-13 for x in the equation z=x+13.

$$z=a-13+13$$

Calculate z from z=a-13+13.

$$z=a$$

The system is now solved.

$$x=a-13 y=\frac{96}{7}-\frac{6}{7}a z=a$$