Solve {l}{3{(6-2x-2z)}+6-6z+6x+24=0}{y=18-6x-6z+6-6z+24}{text{Solvefor}atext{where}}{a=y}

$$\left. \begin{array} { l } { 3 {(6 - 2 x - 2 z)} + 6 - 6 z + 6 x + 24 = 0 }\\ { y = 18 - 6 x - 6 z + 6 - 6 z + 24 }\\ { \text{Solve for } a \text{ where} } \\ { a = y } \end{array} \right.$$

Solve for x, y, z

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

$$y=a$$

$$z=4$$

Short Steps Using Substitution

Reorder the equations.

$$y=18-6x-6z+6-6z+24 3\left(6-2x-2z\right)+6-6z+6x+24=0 a=y$$

Calculate y from y=18-6x-6z+6-6z+24.

$$y=48-6x-12z$$

Substitute 48-6x-12z for y in the equation a=y.

$$a=48-6x-12z$$

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

$$z=4 x=8-\frac{1}{6}a-2z$$

Substitute 4 for z in the equation x=8-\frac{1}{6}a-2z.

$$x=8-\frac{1}{6}a-2\times 4$$

Calculate x from x=8-\frac{1}{6}a-2\times 4.

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

Substitute 4 for z and -\frac{1}{6}a for x in the equation y=48-6x-12z.

$$y=48-6\left(-\frac{1}{6}\right)a-12\times 4$$

Calculate y from y=48-6\left(-\frac{1}{6}\right)a-12\times 4.

$$y=a$$

The system is now solved.

$$x=-\frac{1}{6}a y=a z=4$$