Solve {l}{2x+2y=85}{3x+2x=118}

$$\left. \begin{array} { l } { 2 x + 2 y = 85 } \\ { 3 x + 2 x = 118 } \end{array} \right.$$

Solve for x, y

$$x = \frac{118}{5} = 23\frac{3}{5} = 23.6$$

$$y = \frac{189}{10} = 18\frac{9}{10} = 18.9$$

Solution Steps

Consider the second equation. Combine 3x and 2x to get 5x.

$$5x=118$$

Divide both sides by 5.

$$x=\frac{118}{5}$$

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

$$2\times \frac{118}{5}+2y=85$$

Multiply 2 and \frac{118}{5} to get \frac{236}{5}.

$$\frac{236}{5}+2y=85$$

Subtract \frac{236}{5} from both sides.

$$2y=85-\frac{236}{5}$$

Subtract \frac{236}{5} from 85 to get \frac{189}{5}.

$$2y=\frac{189}{5}$$

Divide both sides by 2.

$$y=\frac{\frac{189}{5}}{2}$$

Express \frac{\frac{189}{5}}{2} as a single fraction.

$$y=\frac{189}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$y=\frac{189}{10}$$

The system is now solved.

$$x=\frac{118}{5} y=\frac{189}{10}$$