Solve {l}{5x+2=11}{2x-3y=12}

$$\left\{ \begin{array} { l } { 5 x + 2 = 11 } \\ { 2 x - 3 y = 12 } \end{array} \right.$$

Solve for x, y

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

$$y = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Solution Steps

Consider the first equation. Subtract 2 from both sides.

$$5x=11-2$$

Subtract 2 from 11 to get 9.

$$5x=9$$

Divide both sides by 5.

$$x=\frac{9}{5}$$

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

$$2\times \frac{9}{5}-3y=12$$

Multiply 2 and \frac{9}{5} to get \frac{18}{5}.

$$\frac{18}{5}-3y=12$$

Subtract \frac{18}{5} from both sides.

$$-3y=12-\frac{18}{5}$$

Subtract \frac{18}{5} from 12 to get \frac{42}{5}.

$$-3y=\frac{42}{5}$$

Divide both sides by -3.

$$y=\frac{\frac{42}{5}}{-3}$$

Express \frac{\frac{42}{5}}{-3} as a single fraction.

$$y=\frac{42}{5\left(-3\right)}$$

Multiply 5 and -3 to get -15.

$$y=\frac{42}{-15}$$

Reduce the fraction \frac{42}{-15} to lowest terms by extracting and canceling out 3.

$$y=-\frac{14}{5}$$

The system is now solved.

$$x=\frac{9}{5} y=-\frac{14}{5}$$