Solve {l}{20x+8x=428}{12x+2y=198}

$$\left\{ \begin{array} { l } { 20 x + 8 x = 428 } \\ { 12 x + 2 y = 198 } \end{array} \right.$$

Solve for x, y

$$x = \frac{107}{7} = 15\frac{2}{7} \approx 15.285714286$$

$$y = \frac{51}{7} = 7\frac{2}{7} \approx 7.285714286$$

Solution Steps

Consider the first equation. Combine 20x and 8x to get 28x.

$$28x=428$$

Divide both sides by 28.

$$x=\frac{428}{28}$$

Reduce the fraction \frac{428}{28} to lowest terms by extracting and canceling out 4.

$$x=\frac{107}{7}$$

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

$$12\times \frac{107}{7}+2y=198$$

Multiply 12 and \frac{107}{7} to get \frac{1284}{7}.

$$\frac{1284}{7}+2y=198$$

Subtract \frac{1284}{7} from both sides.

$$2y=198-\frac{1284}{7}$$

Subtract \frac{1284}{7} from 198 to get \frac{102}{7}.

$$2y=\frac{102}{7}$$

Divide both sides by 2.

$$y=\frac{\frac{102}{7}}{2}$$

Express \frac{\frac{102}{7}}{2} as a single fraction.

$$y=\frac{102}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$y=\frac{102}{14}$$

Reduce the fraction \frac{102}{14} to lowest terms by extracting and canceling out 2.

$$y=\frac{51}{7}$$

The system is now solved.

$$x=\frac{107}{7} y=\frac{51}{7}$$