Solve {l}{2x+2y=4}{5x=8}

$$\left\{ \begin{array} { l } { 2 x + 2 y = 4 } \\ { 5 x = 8 } \end{array} \right.$$

Solve for x, y

$$x = \frac{8}{5} = 1\frac{3}{5} = 1.6$$

$$y=\frac{2}{5}=0.4$$

Solution Steps

Consider the second equation. Divide both sides by 5.

$$x=\frac{8}{5}$$

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

$$2\times \frac{8}{5}+2y=4$$

Multiply 2 and \frac{8}{5} to get \frac{16}{5}.

$$\frac{16}{5}+2y=4$$

Subtract \frac{16}{5} from both sides.

$$2y=4-\frac{16}{5}$$

Subtract \frac{16}{5} from 4 to get \frac{4}{5}.

$$2y=\frac{4}{5}$$

Divide both sides by 2.

$$y=\frac{\frac{4}{5}}{2}$$

Express \frac{\frac{4}{5}}{2} as a single fraction.

$$y=\frac{4}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$y=\frac{4}{10}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

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

The system is now solved.

$$x=\frac{8}{5} y=\frac{2}{5}$$