Solve {l}{-2y=6}{z=6x-4y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { -2 y = 6 }\\ { z = 6 x - 4 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a-12}{6}$$

$$y=-3$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=6x-4y -2y=6 a=z$$

Substitute 6x-4y for z in the equation a=z.

$$a=6x-4y$$

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

$$y=-3 x=\frac{1}{6}a+\frac{2}{3}y$$

Substitute -3 for y in the equation x=\frac{1}{6}a+\frac{2}{3}y.

$$x=\frac{1}{6}a+\frac{2}{3}\left(-3\right)$$

Calculate x from x=\frac{1}{6}a+\frac{2}{3}\left(-3\right).

$$x=-2+\frac{1}{6}a$$

Substitute -3 for y and -2+\frac{1}{6}a for x in the equation z=6x-4y.

$$z=6\left(-2+\frac{1}{6}a\right)-4\left(-3\right)$$

Calculate z from z=6\left(-2+\frac{1}{6}a\right)-4\left(-3\right).

$$z=a$$

The system is now solved.

$$x=-2+\frac{1}{6}a y=-3 z=a$$