Solve {l}{2x+3y=19}{3x-14=2}

$$\left. \begin{array} { l } { 2 x + 3 y = 19 } \\ { 3 x - 14 = 2 } \end{array} \right.$$

Solve for x, y

$$x = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

$$y = \frac{25}{9} = 2\frac{7}{9} \approx 2.777777778$$

Solution Steps

Consider the second equation. Add 14 to both sides.

$$3x=2+14$$

Add 2 and 14 to get 16.

$$3x=16$$

Divide both sides by 3.

$$x=\frac{16}{3}$$

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

$$2\times \frac{16}{3}+3y=19$$

Multiply 2 and \frac{16}{3} to get \frac{32}{3}.

$$\frac{32}{3}+3y=19$$

Subtract \frac{32}{3} from both sides.

$$3y=19-\frac{32}{3}$$

Subtract \frac{32}{3} from 19 to get \frac{25}{3}.

$$3y=\frac{25}{3}$$

Divide both sides by 3.

$$y=\frac{\frac{25}{3}}{3}$$

Express \frac{\frac{25}{3}}{3} as a single fraction.

$$y=\frac{25}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$y=\frac{25}{9}$$

The system is now solved.

$$x=\frac{16}{3} y=\frac{25}{9}$$