Solve {l}{x+y=200}{1.05+1.15y=225}

$$\left\{ \begin{array} { l } { x + y = 200 } \\ { 1.05 + 1.15 y = 225 } \end{array} \right.$$

Solve for x, y

$$x = \frac{121}{23} = 5\frac{6}{23} \approx 5.260869565$$

$$y = \frac{4479}{23} = 194\frac{17}{23} \approx 194.739130435$$

Solution Steps

Consider the second equation. Subtract 1.05 from both sides.

$$1.15y=225-1.05$$

Subtract 1.05 from 225 to get 223.95.

$$1.15y=223.95$$

Divide both sides by 1.15.

$$y=\frac{223.95}{1.15}$$

Expand \frac{223.95}{1.15} by multiplying both numerator and the denominator by 100.

$$y=\frac{22395}{115}$$

Reduce the fraction \frac{22395}{115} to lowest terms by extracting and canceling out 5.

$$y=\frac{4479}{23}$$

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

$$x+\frac{4479}{23}=200$$

Subtract \frac{4479}{23} from both sides.

$$x=200-\frac{4479}{23}$$

Subtract \frac{4479}{23} from 200 to get \frac{121}{23}.

$$x=\frac{121}{23}$$

The system is now solved.

$$x=\frac{121}{23} y=\frac{4479}{23}$$