Solve {l}{0.15x+0.08y=1}{0.5x+0.3x=2}

$$\left\{ \begin{array} { l } { 0.15 x + 0.08 y = 1 } \\ { 0.5 x + 0.3 x = 2 } \end{array} \right.$$

Solve for x, y

$$x=2.5$$

$$y=7.8125$$

Solution Steps

Consider the second equation. Combine 0.5x and 0.3x to get 0.8x.

$$0.8x=2$$

Divide both sides by 0.8.

$$x=\frac{2}{0.8}$$

Expand \frac{2}{0.8} by multiplying both numerator and the denominator by 10.

$$x=\frac{20}{8}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{5}{2}$$

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

$$0.15\times \frac{5}{2}+0.08y=1$$

Multiply 0.15 and \frac{5}{2} to get \frac{3}{8}.

$$\frac{3}{8}+0.08y=1$$

Subtract \frac{3}{8} from both sides.

$$0.08y=1-\frac{3}{8}$$

Subtract \frac{3}{8} from 1 to get \frac{5}{8}.

$$0.08y=\frac{5}{8}$$

Divide both sides by 0.08.

$$y=\frac{\frac{5}{8}}{0.08}$$

Express \frac{\frac{5}{8}}{0.08} as a single fraction.

$$y=\frac{5}{8\times 0.08}$$

Multiply 8 and 0.08 to get 0.64.

$$y=\frac{5}{0.64}$$

Expand \frac{5}{0.64} by multiplying both numerator and the denominator by 100.

$$y=\frac{500}{64}$$

Reduce the fraction \frac{500}{64} to lowest terms by extracting and canceling out 4.

$$y=\frac{125}{16}$$

The system is now solved.

$$x=\frac{5}{2} y=\frac{125}{16}$$