Solve {l}{2300x+1200y=1880}{2300x*100+1200*80/100=18780}

$$\left. \begin{array} { l } { 2300 x + 1200 y = 1880 } \\ { 2300 x \times 100 + 1200 \times \frac { 80 } { 100 } = 18780 } \end{array} \right.$$

Solve for x, y

$$x=\frac{891}{11500}\approx 0.077478261$$

$$y = \frac{8509}{6000} = 1\frac{2509}{6000} \approx 1.418166667$$

Solution Steps

Consider the second equation. Multiply 2300 and 100 to get 230000.

$$230000x+1200\times \frac{80}{100}=18780$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$230000x+1200\times \frac{4}{5}=18780$$

Multiply 1200 and \frac{4}{5} to get 960.

$$230000x+960=18780$$

Subtract 960 from both sides.

$$230000x=18780-960$$

Subtract 960 from 18780 to get 17820.

$$230000x=17820$$

Divide both sides by 230000.

$$x=\frac{17820}{230000}$$

Reduce the fraction \frac{17820}{230000} to lowest terms by extracting and canceling out 20.

$$x=\frac{891}{11500}$$

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

$$2300\times \frac{891}{11500}+1200y=1880$$

Multiply 2300 and \frac{891}{11500} to get \frac{891}{5}.

$$\frac{891}{5}+1200y=1880$$

Subtract \frac{891}{5} from both sides.

$$1200y=1880-\frac{891}{5}$$

Subtract \frac{891}{5} from 1880 to get \frac{8509}{5}.

$$1200y=\frac{8509}{5}$$

Divide both sides by 1200.

$$y=\frac{\frac{8509}{5}}{1200}$$

Express \frac{\frac{8509}{5}}{1200} as a single fraction.

$$y=\frac{8509}{5\times 1200}$$

Multiply 5 and 1200 to get 6000.

$$y=\frac{8509}{6000}$$

The system is now solved.

$$x=\frac{891}{11500} y=\frac{8509}{6000}$$