Solve {l}{7x+4=35}{4y+2x=200}

$$\left. \begin{array} { l } { 7 x + 4 = 35 } \\ { 4 y + 2 x = 200 } \end{array} \right.$$

Solve for x, y

$$x = \frac{31}{7} = 4\frac{3}{7} \approx 4.428571429$$

$$y = \frac{669}{14} = 47\frac{11}{14} \approx 47.785714286$$

Solution Steps

Consider the first equation. Subtract 4 from both sides.

$$7x=35-4$$

Subtract 4 from 35 to get 31.

$$7x=31$$

Divide both sides by 7.

$$x=\frac{31}{7}$$

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

$$4y+2\times \frac{31}{7}=200$$

Multiply 2 and \frac{31}{7} to get \frac{62}{7}.

$$4y+\frac{62}{7}=200$$

Subtract \frac{62}{7} from both sides.

$$4y=200-\frac{62}{7}$$

Subtract \frac{62}{7} from 200 to get \frac{1338}{7}.

$$4y=\frac{1338}{7}$$

Divide both sides by 4.

$$y=\frac{\frac{1338}{7}}{4}$$

Express \frac{\frac{1338}{7}}{4} as a single fraction.

$$y=\frac{1338}{7\times 4}$$

Multiply 7 and 4 to get 28.

$$y=\frac{1338}{28}$$

Reduce the fraction \frac{1338}{28} to lowest terms by extracting and canceling out 2.

$$y=\frac{669}{14}$$

The system is now solved.

$$x=\frac{31}{7} y=\frac{669}{14}$$