Solve {l}{x+7/3=8}{x/3+y/2=7/9}

$$\left. \begin{array} { l } { x + \frac { 7 } { 3 } = 8 } \\ { \frac { x } { 3 } + \frac { y } { 2 } = \frac { 7 } { 9 } } \end{array} \right.$$

Solve for x, y

$$x = \frac{17}{3} = 5\frac{2}{3} \approx 5.666666667$$

$$y = -\frac{20}{9} = -2\frac{2}{9} \approx -2.222222222$$

Solution Steps

Consider the first equation. Subtract \frac{7}{3} from both sides.

$$x=8-\frac{7}{3}$$

Subtract \frac{7}{3} from 8 to get \frac{17}{3}.

$$x=\frac{17}{3}$$

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

$$\frac{\frac{17}{3}}{3}+\frac{y}{2}=\frac{7}{9}$$

Multiply both sides of the equation by 18, the least common multiple of 3,2,9.

$$6\times \frac{17}{3}+9y=14$$

Multiply 6 and \frac{17}{3} to get 34.

$$34+9y=14$$

Subtract 34 from both sides.

$$9y=14-34$$

Subtract 34 from 14 to get -20.

$$9y=-20$$

Divide both sides by 9.

$$y=-\frac{20}{9}$$

The system is now solved.

$$x=\frac{17}{3} y=-\frac{20}{9}$$