Solve {l}{2/3(x+4)-1/2y=9/2}{x+2y-1/3(3x-2)=frac{-4}{3}}

$$\left. \begin{array} { l } { \frac { 2 } { 3 } ( x + 4 ) - \frac { 1 } { 2 } y = \frac { 9 } { 2 } } \\ { x + 2 y - \frac { 1 } { 3 } ( 3 x - 2 ) = \frac { - 4 } { 3 } } \end{array} \right.$$

Solve for x, y

$$x=2$$

$$y=-1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{2}{3} by x+4.

$$\frac{2}{3}x+\frac{8}{3}-\frac{1}{2}y=\frac{9}{2}$$

Subtract \frac{8}{3} from both sides.

$$\frac{2}{3}x-\frac{1}{2}y=\frac{9}{2}-\frac{8}{3}$$

Subtract \frac{8}{3} from \frac{9}{2} to get \frac{11}{6}.

$$\frac{2}{3}x-\frac{1}{2}y=\frac{11}{6}$$

Consider the second equation. Use the distributive property to multiply -\frac{1}{3} by 3x-2.

$$x+2y-x+\frac{2}{3}=\frac{-4}{3}$$

Combine x and -x to get 0.

$$2y+\frac{2}{3}=\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$2y+\frac{2}{3}=-\frac{4}{3}$$

Subtract \frac{2}{3} from both sides.

$$2y=-\frac{4}{3}-\frac{2}{3}$$

Subtract \frac{2}{3} from -\frac{4}{3} to get -2.

$$2y=-2$$

Divide both sides by 2.

$$y=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$y=-1$$

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

$$\frac{2}{3}x-\frac{1}{2}\left(-1\right)=\frac{11}{6}$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$\frac{2}{3}x+\frac{1}{2}=\frac{11}{6}$$

Subtract \frac{1}{2} from both sides.

$$\frac{2}{3}x=\frac{11}{6}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{11}{6} to get \frac{4}{3}.

$$\frac{2}{3}x=\frac{4}{3}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x=\frac{4}{3}\times \frac{3}{2}$$

Multiply \frac{4}{3} and \frac{3}{2} to get 2.

$$x=2$$

The system is now solved.

$$x=2 y=-1$$