Solve {l}{8x-2y=28}{z=x+4y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 8 x - 2 y = 28 }\\ { z = x + 4 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a+56}{17}$$

$$y=\frac{4a-14}{17}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=x+4y 8x-2y=28 a=z$$

Substitute x+4y for z in the equation a=z.

$$a=x+4y$$

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

$$y=-14+4x x=a-4y$$

Substitute -14+4x for y in the equation x=a-4y.

$$x=a-4\left(-14+4x\right)$$

Solve x=a-4\left(-14+4x\right) for x.

$$x=\frac{56}{17}+\frac{1}{17}a$$

Substitute \frac{56}{17}+\frac{1}{17}a for x in the equation y=-14+4x.

$$y=-14+4\left(\frac{56}{17}+\frac{1}{17}a\right)$$

Calculate y from y=-14+4\left(\frac{56}{17}+\frac{1}{17}a\right).

$$y=-\frac{14}{17}+\frac{4}{17}a$$

Substitute -\frac{14}{17}+\frac{4}{17}a for y and \frac{56}{17}+\frac{1}{17}a for x in the equation z=x+4y.

$$z=\frac{56}{17}+\frac{1}{17}a+4\left(-\frac{14}{17}+\frac{4}{17}a\right)$$

Calculate z from z=\frac{56}{17}+\frac{1}{17}a+4\left(-\frac{14}{17}+\frac{4}{17}a\right).

$$z=a$$

The system is now solved.

$$x=\frac{56}{17}+\frac{1}{17}a y=-\frac{14}{17}+\frac{4}{17}a z=a$$