Solve {l}{x/3{(8-x)}=11+y}{z=x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { x / 3 {(8 - x)} = 11 + y }\\ { z = x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=a$$

$$y=\frac{a\left(8-a\right)-33}{3}$$

$$z=a$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$x\left(8-x\right)=33+3y z=x a=z$$

Reorder the equations.

$$z=x x\left(8-x\right)=33+3y a=z$$

Substitute x for z in the equation a=z.

$$a=x$$

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

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

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

$$y=\frac{8}{3}a-\frac{1}{3}a^{2}-11$$

Substitute a for x in the equation z=x.

$$z=a$$

The system is now solved.

$$x=a y=\frac{8}{3}a-\frac{1}{3}a^{2}-11 z=a$$