Solve {l}{850x=50y}{z=100x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 850 x = 50 y }\\ { z = 100 x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a}{100}$$

$$y=\frac{17a}{100}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=100x 850x=50y a=z$$

Substitute 100x for z in the equation a=z.

$$a=100x$$

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

$$y=17x x=\frac{1}{100}a$$

Substitute \frac{1}{100}a for x in the equation y=17x.

$$y=17\times \frac{1}{100}a$$

Calculate y from y=17\times \frac{1}{100}a.

$$y=\frac{17}{100}a$$

Substitute \frac{1}{100}a for x in the equation z=100x.

$$z=100\times \frac{1}{100}a$$

Calculate z from z=100\times \frac{1}{100}a.

$$z=a$$

The system is now solved.

$$x=\frac{1}{100}a y=\frac{17}{100}a z=a$$