Solve {l}{2x+3y=13}{5x+2(x)=16}

$$\left. \begin{array} { l } { 2 x + 3 y = 13 } \\ { 5 x + 2 ( x ) = 16 } \end{array} \right.$$

Solve for x, y

$$x = \frac{16}{7} = 2\frac{2}{7} \approx 2.285714286$$

$$y = \frac{59}{21} = 2\frac{17}{21} \approx 2.80952381$$

Solution Steps

Consider the second equation. Combine 5x and 2x to get 7x.

$$7x=16$$

Divide both sides by 7.

$$x=\frac{16}{7}$$

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

$$2\times \frac{16}{7}+3y=13$$

Multiply 2 and \frac{16}{7} to get \frac{32}{7}.

$$\frac{32}{7}+3y=13$$

Subtract \frac{32}{7} from both sides.

$$3y=13-\frac{32}{7}$$

Subtract \frac{32}{7} from 13 to get \frac{59}{7}.

$$3y=\frac{59}{7}$$

Divide both sides by 3.

$$y=\frac{\frac{59}{7}}{3}$$

Express \frac{\frac{59}{7}}{3} as a single fraction.

$$y=\frac{59}{7\times 3}$$

Multiply 7 and 3 to get 21.

$$y=\frac{59}{21}$$

The system is now solved.

$$x=\frac{16}{7} y=\frac{59}{21}$$