Solve {l}{3x-y/2-2x+6y/3=1}{x-3/5+2x/3=frac{30+2}{2}}

$$\left\{ \begin{array} { l } { \frac { 3 x - y } { 2 } - \frac { 2 x + 6 y } { 3 } = 1 } \\ { \frac { x - 3 } { 5 } + \frac { 2 x } { 3 } = \frac { 30 + 2 } { 2 } } \end{array} \right.$$

Solve for x, y

$$x = \frac{249}{13} = 19\frac{2}{13} \approx 19.153846154$$

$$y = \frac{389}{65} = 5\frac{64}{65} \approx 5.984615385$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 30, the least common multiple of 5,3,2.

$$6\left(x-3\right)+10\times 2x=15\left(30+2\right)$$

Use the distributive property to multiply 6 by x-3.

$$6x-18+10\times 2x=15\left(30+2\right)$$

Multiply 10 and 2 to get 20.

$$6x-18+20x=15\left(30+2\right)$$

Combine 6x and 20x to get 26x.

$$26x-18=15\left(30+2\right)$$

Add 30 and 2 to get 32.

$$26x-18=15\times 32$$

Multiply 15 and 32 to get 480.

$$26x-18=480$$

Add 18 to both sides.

$$26x=480+18$$

Add 480 and 18 to get 498.

$$26x=498$$

Divide both sides by 26.

$$x=\frac{498}{26}$$

Reduce the fraction \frac{498}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{249}{13}$$

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

$$\frac{3\times \frac{249}{13}-y}{2}-\frac{2\times \frac{249}{13}+6y}{3}=1$$

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(3\times \frac{249}{13}-y\right)-2\left(2\times \frac{249}{13}+6y\right)=6$$

Multiply 3 and \frac{249}{13} to get \frac{747}{13}.

$$3\left(\frac{747}{13}-y\right)-2\left(2\times \frac{249}{13}+6y\right)=6$$

Use the distributive property to multiply 3 by \frac{747}{13}-y.

$$\frac{2241}{13}-3y-2\left(2\times \frac{249}{13}+6y\right)=6$$

Multiply 2 and \frac{249}{13} to get \frac{498}{13}.

$$\frac{2241}{13}-3y-2\left(\frac{498}{13}+6y\right)=6$$

Use the distributive property to multiply -2 by \frac{498}{13}+6y.

$$\frac{2241}{13}-3y-\frac{996}{13}-12y=6$$

Subtract \frac{996}{13} from \frac{2241}{13} to get \frac{1245}{13}.

$$\frac{1245}{13}-3y-12y=6$$

Combine -3y and -12y to get -15y.

$$\frac{1245}{13}-15y=6$$

Subtract \frac{1245}{13} from both sides.

$$-15y=6-\frac{1245}{13}$$

Subtract \frac{1245}{13} from 6 to get -\frac{1167}{13}.

$$-15y=-\frac{1167}{13}$$

Divide both sides by -15.

$$y=\frac{-\frac{1167}{13}}{-15}$$

Express \frac{-\frac{1167}{13}}{-15} as a single fraction.

$$y=\frac{-1167}{13\left(-15\right)}$$

Multiply 13 and -15 to get -195.

$$y=\frac{-1167}{-195}$$

Reduce the fraction \frac{-1167}{-195} to lowest terms by extracting and canceling out -3.

$$y=\frac{389}{65}$$

The system is now solved.

$$x=\frac{249}{13} y=\frac{389}{65}$$