Solve {l}{12000=20x+45x}{text{Solvefor}ytext{where}}{y=10{(800-4x)}}

$$\left. \begin{array} { l } { 12000 = 20 x + 45 x }\\ { \text{Solve for } y \text{ where} } \\ { y = 10 {(800 - 4 x)} } \end{array} \right.$$

Solve for x, y

$$y = \frac{8000}{13} = 615\frac{5}{13} \approx 615.384615385$$

Solution Steps

Consider the first equation. Combine 20x and 45x to get 65x.

$$12000=65x$$

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

$$65x=12000$$

Divide both sides by 65.

$$x=\frac{12000}{65}$$

Reduce the fraction \frac{12000}{65} to lowest terms by extracting and canceling out 5.

$$x=\frac{2400}{13}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=10\left(800-4\times \frac{2400}{13}\right)$$

Multiply -4 and \frac{2400}{13} to get -\frac{9600}{13}.

$$y=10\left(800-\frac{9600}{13}\right)$$

Subtract \frac{9600}{13} from 800 to get \frac{800}{13}.

$$y=10\times \frac{800}{13}$$

Multiply 10 and \frac{800}{13} to get \frac{8000}{13}.

$$y=\frac{8000}{13}$$

The system is now solved.

$$x=\frac{2400}{13} y=\frac{8000}{13}$$