Solve {l}{x-y=2}{z=4x-3y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { x - y = 2 }\\ { z = 4 x - 3 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=a-6$$

$$y=a-8$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=4x-3y x-y=2 a=z$$

Substitute 4x-3y for z in the equation a=z.

$$a=4x-3y$$

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

$$y=x-2 x=\frac{1}{4}a+\frac{3}{4}y$$

Substitute x-2 for y in the equation x=\frac{1}{4}a+\frac{3}{4}y.

$$x=\frac{1}{4}a+\frac{3}{4}\left(x-2\right)$$

Solve x=\frac{1}{4}a+\frac{3}{4}\left(x-2\right) for x.

$$x=-6+a$$

Substitute -6+a for x in the equation y=x-2.

$$y=-6+a-2$$

Calculate y from y=-6+a-2.

$$y=-8+a$$

Substitute -8+a for y and -6+a for x in the equation z=4x-3y.

$$z=4\left(-6+a\right)-3\left(-8+a\right)$$

Calculate z from z=4\left(-6+a\right)-3\left(-8+a\right).

$$z=a$$

The system is now solved.

$$x=-6+a y=-8+a z=a$$