Solve {l}{7/9y+2/3y=6800}{2/9x=1/3y-100}

$$\left. \begin{array} { l } { \frac { 7 } { 9 } y + \frac { 2 } { 3 } y = 6800 } \\ { \frac { 2 } { 9 } x = \frac { 1 } { 3 } y - 100 } \end{array} \right.$$

Solve for y, x

$$x = \frac{85950}{13} = 6611\frac{7}{13} \approx 6611.538461538$$

$$y = \frac{61200}{13} = 4707\frac{9}{13} \approx 4707.692307692$$

Solution Steps

Consider the first equation. Combine \frac{7}{9}y and \frac{2}{3}y to get \frac{13}{9}y.

$$\frac{13}{9}y=6800$$

Multiply both sides by \frac{9}{13}, the reciprocal of \frac{13}{9}.

$$y=6800\times \frac{9}{13}$$

Multiply 6800 and \frac{9}{13} to get \frac{61200}{13}.

$$y=\frac{61200}{13}$$

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

$$\frac{2}{9}x=\frac{1}{3}\times \frac{61200}{13}-100$$

Multiply \frac{1}{3} and \frac{61200}{13} to get \frac{20400}{13}.

$$\frac{2}{9}x=\frac{20400}{13}-100$$

Subtract 100 from \frac{20400}{13} to get \frac{19100}{13}.

$$\frac{2}{9}x=\frac{19100}{13}$$

Multiply both sides by \frac{9}{2}, the reciprocal of \frac{2}{9}.

$$x=\frac{19100}{13}\times \frac{9}{2}$$

Multiply \frac{19100}{13} and \frac{9}{2} to get \frac{85950}{13}.

$$x=\frac{85950}{13}$$

The system is now solved.

$$y=\frac{61200}{13} x=\frac{85950}{13}$$