Solve {l}{x-6=-1/3}{x-3/5+y=x+21/5}

$$\left\{ \begin{array} { l } { x - 6 = - \frac { 1 } { 3 } } \\ { \frac { x - 3 } { 5 } + y = x + \frac { 21 } { 5 } } \end{array} \right.$$

Solve for x, y

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

$$y = \frac{28}{3} = 9\frac{1}{3} \approx 9.333333333$$

Solution Steps

Consider the first equation. Add 6 to both sides.

$$x=-\frac{1}{3}+6$$

Add -\frac{1}{3} and 6 to get \frac{17}{3}.

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

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

$$\frac{\frac{17}{3}-3}{5}+y=\frac{17}{3}+\frac{21}{5}$$

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\left(\frac{17}{3}-3\right)+15y=85+63$$

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

$$3\times \frac{8}{3}+15y=85+63$$

Multiply 3 and \frac{8}{3} to get 8.

$$8+15y=85+63$$

Add 85 and 63 to get 148.

$$8+15y=148$$

Subtract 8 from both sides.

$$15y=148-8$$

Subtract 8 from 148 to get 140.

$$15y=140$$

Divide both sides by 15.

$$y=\frac{140}{15}$$

Reduce the fraction \frac{140}{15} to lowest terms by extracting and canceling out 5.

$$y=\frac{28}{3}$$

The system is now solved.

$$x=\frac{17}{3} y=\frac{28}{3}$$