Solve {l}{2x+5y=13}{5x-14=9}

$$\left. \begin{array} { l } { 2 x + 5 y = 13 } \\ { 5 x - 14 = 9 } \end{array} \right.$$

Solve for x, y

$$x = \frac{23}{5} = 4\frac{3}{5} = 4.6$$

$$y=\frac{19}{25}=0.76$$

Solution Steps

Consider the second equation. Add 14 to both sides.

$$5x=9+14$$

Add 9 and 14 to get 23.

$$5x=23$$

Divide both sides by 5.

$$x=\frac{23}{5}$$

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

$$2\times \frac{23}{5}+5y=13$$

Multiply 2 and \frac{23}{5} to get \frac{46}{5}.

$$\frac{46}{5}+5y=13$$

Subtract \frac{46}{5} from both sides.

$$5y=13-\frac{46}{5}$$

Subtract \frac{46}{5} from 13 to get \frac{19}{5}.

$$5y=\frac{19}{5}$$

Divide both sides by 5.

$$y=\frac{\frac{19}{5}}{5}$$

Express \frac{\frac{19}{5}}{5} as a single fraction.

$$y=\frac{19}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$y=\frac{19}{25}$$

The system is now solved.

$$x=\frac{23}{5} y=\frac{19}{25}$$