Solve {l}{3=frac{78x+216{(309-x)}}{1000}}{y=0}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 3 = \frac{78 x + 216 {(309 - x)}}{1000} }\\ { y = 0 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=0$$

Solution Steps

Consider the first equation. Multiply both sides by 1000.

$$3\times 1000=78x+216\left(309-x\right)$$

Multiply 3 and 1000 to get 3000.

$$3000=78x+216\left(309-x\right)$$

Use the distributive property to multiply 216 by 309-x.

$$3000=78x+66744-216x$$

Combine 78x and -216x to get -138x.

$$3000=-138x+66744$$

Swap sides so that all variable terms are on the left hand side.

$$-138x+66744=3000$$

Subtract 66744 from both sides.

$$-138x=3000-66744$$

Subtract 66744 from 3000 to get -63744.

$$-138x=-63744$$

Divide both sides by -138.

$$x=\frac{-63744}{-138}$$

Reduce the fraction \frac{-63744}{-138} to lowest terms by extracting and canceling out -6.

$$x=\frac{10624}{23}$$

The system is now solved.

$$x=\frac{10624}{23} y=0 z=0$$