Solve {l}{4x-6y=48}{z=8x-11y-92}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 4 x - 6 y = 48 }\\ { z = 8 x - 11 y - 92 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{3\left(a+4\right)}{2}$$

$$y=a-4$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=8x-11y-92 4x-6y=48 a=z$$

Substitute 8x-11y-92 for z in the equation a=z.

$$a=8x-11y-92$$

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

$$y=-8+\frac{2}{3}x x=\frac{23}{2}+\frac{11}{8}y+\frac{1}{8}a$$

Substitute -8+\frac{2}{3}x for y in the equation x=\frac{23}{2}+\frac{11}{8}y+\frac{1}{8}a.

$$x=\frac{23}{2}+\frac{11}{8}\left(-8+\frac{2}{3}x\right)+\frac{1}{8}a$$

Solve x=\frac{23}{2}+\frac{11}{8}\left(-8+\frac{2}{3}x\right)+\frac{1}{8}a for x.

$$x=6+\frac{3}{2}a$$

Substitute 6+\frac{3}{2}a for x in the equation y=-8+\frac{2}{3}x.

$$y=-8+\frac{2}{3}\left(6+\frac{3}{2}a\right)$$

Calculate y from y=-8+\frac{2}{3}\left(6+\frac{3}{2}a\right).

$$y=-4+a$$

Substitute -4+a for y and 6+\frac{3}{2}a for x in the equation z=8x-11y-92.

$$z=8\left(6+\frac{3}{2}a\right)-11\left(-4+a\right)-92$$

Calculate z from z=8\left(6+\frac{3}{2}a\right)-11\left(-4+a\right)-92.

$$z=a$$

The system is now solved.

$$x=6+\frac{3}{2}a y=-4+a z=a$$