Solve {l}{y=x/2}{z={(3x)}}{text{Solvefor}atext{where}}{a=z}

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

Solve for x, y, z

$$x=\frac{a}{3}$$

$$y=\frac{a}{6}$$

$$z=a$$

Short Steps Using Substitution

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

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

Solve 2y=x for x.

$$x=2y$$

Substitute 2y for x in the equation z=3x.

$$z=3\times 2y$$

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

$$y=\frac{1}{6}z z=a$$

Substitute a for z in the equation y=\frac{1}{6}z.

$$y=\frac{1}{6}a$$

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

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

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

$$x=\frac{1}{3}a$$

The system is now solved.

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