Solve {l}{7x+9y=95}{z=x+y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 7 x + 9 y = 95 }\\ { z = x + y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{9a-95}{2}$$

$$y=\frac{95-7a}{2}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=x+y 7x+9y=95 a=z$$

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

$$a=x+y$$

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

$$y=-\frac{7}{9}x+\frac{95}{9} x=a-y$$

Substitute -\frac{7}{9}x+\frac{95}{9} for y in the equation x=a-y.

$$x=a-\left(-\frac{7}{9}x+\frac{95}{9}\right)$$

Solve x=a-\left(-\frac{7}{9}x+\frac{95}{9}\right) for x.

$$x=-\frac{95}{2}+\frac{9}{2}a$$

Substitute -\frac{95}{2}+\frac{9}{2}a for x in the equation y=-\frac{7}{9}x+\frac{95}{9}.

$$y=-\frac{7}{9}\left(-\frac{95}{2}+\frac{9}{2}a\right)+\frac{95}{9}$$

Calculate y from y=-\frac{7}{9}\left(-\frac{95}{2}+\frac{9}{2}a\right)+\frac{95}{9}.

$$y=\frac{95}{2}-\frac{7}{2}a$$

Substitute \frac{95}{2}-\frac{7}{2}a for y and -\frac{95}{2}+\frac{9}{2}a for x in the equation z=x+y.

$$z=-\frac{95}{2}+\frac{9}{2}a+\frac{95}{2}-\frac{7}{2}a$$

Calculate z from z=-\frac{95}{2}+\frac{9}{2}a+\frac{95}{2}-\frac{7}{2}a.

$$z=a$$

The system is now solved.

$$x=-\frac{95}{2}+\frac{9}{2}a y=\frac{95}{2}-\frac{7}{2}a z=a$$