Solve {l}{7x+2/5y=4/3}{3/4x-6/7x=frac{2}{5}}

$$\left. \begin{array} { l } { 7 x + \frac { 2 } { 5 } y = \frac { 4 } { 3 } } \\ { \frac { 3 } { 4 } x - \frac { 6 } { 7 } x = \frac { 2 } { 5 } } \end{array} \right.$$

Solve for x, y

$$x = -\frac{56}{15} = -3\frac{11}{15} \approx -3.733333333$$

$$y = \frac{206}{3} = 68\frac{2}{3} \approx 68.666666667$$

Solution Steps

Consider the second equation. Combine \frac{3}{4}x and -\frac{6}{7}x to get -\frac{3}{28}x.

$$-\frac{3}{28}x=\frac{2}{5}$$

Multiply both sides by -\frac{28}{3}, the reciprocal of -\frac{3}{28}.

$$x=\frac{2}{5}\left(-\frac{28}{3}\right)$$

Multiply \frac{2}{5} and -\frac{28}{3} to get -\frac{56}{15}.

$$x=-\frac{56}{15}$$

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

$$7\left(-\frac{56}{15}\right)+\frac{2}{5}y=\frac{4}{3}$$

Multiply 7 and -\frac{56}{15} to get -\frac{392}{15}.

$$-\frac{392}{15}+\frac{2}{5}y=\frac{4}{3}$$

Add \frac{392}{15} to both sides.

$$\frac{2}{5}y=\frac{4}{3}+\frac{392}{15}$$

Add \frac{4}{3} and \frac{392}{15} to get \frac{412}{15}.

$$\frac{2}{5}y=\frac{412}{15}$$

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$y=\frac{412}{15}\times \frac{5}{2}$$

Multiply \frac{412}{15} and \frac{5}{2} to get \frac{206}{3}.

$$y=\frac{206}{3}$$

The system is now solved.

$$x=-\frac{56}{15} y=\frac{206}{3}$$