Solve {l}{12x-y=7}{z=2x+2}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 12 x - y = 7 }\\ { z = 2 x + 2 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

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

$$y=6a-19$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=2x+2 12x-y=7 a=z$$

Substitute 2+2x for z in the equation a=z.

$$a=2+2x$$

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

$$y=12x-7 x=-1+\frac{1}{2}a$$

Substitute -1+\frac{1}{2}a for x in the equation y=12x-7.

$$y=12\left(-1+\frac{1}{2}a\right)-7$$

Calculate y from y=12\left(-1+\frac{1}{2}a\right)-7.

$$y=-19+6a$$

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

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

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

$$z=a$$

The system is now solved.

$$x=-1+\frac{1}{2}a y=-19+6a z=a$$