Solve {l}{2x+3y=22}{9x+4=33}

$$\left. \begin{array} { l } { 2 x + 3 y = 22 } \\ { 9 x + 4 = 33 } \end{array} \right.$$

Solve for x, y

$$x = \frac{29}{9} = 3\frac{2}{9} \approx 3.222222222$$

$$y = \frac{140}{27} = 5\frac{5}{27} \approx 5.185185185$$

Solution Steps

Consider the second equation. Subtract 4 from both sides.

$$9x=33-4$$

Subtract 4 from 33 to get 29.

$$9x=29$$

Divide both sides by 9.

$$x=\frac{29}{9}$$

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

$$2\times \frac{29}{9}+3y=22$$

Multiply 2 and \frac{29}{9} to get \frac{58}{9}.

$$\frac{58}{9}+3y=22$$

Subtract \frac{58}{9} from both sides.

$$3y=22-\frac{58}{9}$$

Subtract \frac{58}{9} from 22 to get \frac{140}{9}.

$$3y=\frac{140}{9}$$

Divide both sides by 3.

$$y=\frac{\frac{140}{9}}{3}$$

Express \frac{\frac{140}{9}}{3} as a single fraction.

$$y=\frac{140}{9\times 3}$$

Multiply 9 and 3 to get 27.

$$y=\frac{140}{27}$$

The system is now solved.

$$x=\frac{29}{9} y=\frac{140}{27}$$