Solve {l}{-8/3x-3/4=3}{-4/3x+6/4y=-4}

$$\left. \begin{array} { l } { - \frac { 8 } { 3 } x - \frac { 3 } { 4 } = 3 } \\ { - \frac { 4 } { 3 } x + \frac { 6 } { 4 } y = - 4 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{45}{32} = -1\frac{13}{32} = -1.40625$$

$$y = -\frac{47}{12} = -3\frac{11}{12} \approx -3.916666667$$

Solution Steps

Consider the first equation. Add \frac{3}{4} to both sides.

$$-\frac{8}{3}x=3+\frac{3}{4}$$

Add 3 and \frac{3}{4} to get \frac{15}{4}.

$$-\frac{8}{3}x=\frac{15}{4}$$

Multiply both sides by -\frac{3}{8}, the reciprocal of -\frac{8}{3}.

$$x=\frac{15}{4}\left(-\frac{3}{8}\right)$$

Multiply \frac{15}{4} and -\frac{3}{8} to get -\frac{45}{32}.

$$x=-\frac{45}{32}$$

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

$$-\frac{4}{3}\left(-\frac{45}{32}\right)+\frac{6}{4}y=-4$$

Multiply -\frac{4}{3} and -\frac{45}{32} to get \frac{15}{8}.

$$\frac{15}{8}+\frac{6}{4}y=-4$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{15}{8}+\frac{3}{2}y=-4$$

Subtract \frac{15}{8} from both sides.

$$\frac{3}{2}y=-4-\frac{15}{8}$$

Subtract \frac{15}{8} from -4 to get -\frac{47}{8}.

$$\frac{3}{2}y=-\frac{47}{8}$$

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

$$y=-\frac{47}{8}\times \frac{2}{3}$$

Multiply -\frac{47}{8} and \frac{2}{3} to get -\frac{47}{12}.

$$y=-\frac{47}{12}$$

The system is now solved.

$$x=-\frac{45}{32} y=-\frac{47}{12}$$