Solve {l}{x+4y/5+2/15(y+1)=2(3+x)/10}{8x-6x/3=-6x+frac{49}{3}}

$$\left\{ \begin{array} { l } { \frac { x + 4 y } { 5 } + \frac { 2 } { 15 } ( y + 1 ) = \frac { 2 ( 3 + x ) } { 10 } } \\ { \frac { 8 x - 6 x } { 3 } = - 6 x + \frac { 49 } { 3 } } \end{array} \right.$$

Solve for x, y

$$x = \frac{49}{20} = 2\frac{9}{20} = 2.45$$

$$y=\frac{1}{2}=0.5$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 3.

$$8x-6x=-18x+49$$

Combine 8x and -6x to get 2x.

$$2x=-18x+49$$

Add 18x to both sides.

$$2x+18x=49$$

Combine 2x and 18x to get 20x.

$$20x=49$$

Divide both sides by 20.

$$x=\frac{49}{20}$$

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

$$\frac{\frac{49}{20}+4y}{5}+\frac{2}{15}\left(y+1\right)=\frac{2\left(3+\frac{49}{20}\right)}{10}$$

Multiply both sides of the equation by 30, the least common multiple of 5,15,10.

$$6\left(\frac{49}{20}+4y\right)+4\left(y+1\right)=3\times 2\left(3+\frac{49}{20}\right)$$

Use the distributive property to multiply 6 by \frac{49}{20}+4y.

$$\frac{147}{10}+24y+4\left(y+1\right)=3\times 2\left(3+\frac{49}{20}\right)$$

Use the distributive property to multiply 4 by y+1.

$$\frac{147}{10}+24y+4y+4=3\times 2\left(3+\frac{49}{20}\right)$$

Combine 24y and 4y to get 28y.

$$\frac{147}{10}+28y+4=3\times 2\left(3+\frac{49}{20}\right)$$

Add \frac{147}{10} and 4 to get \frac{187}{10}.

$$\frac{187}{10}+28y=3\times 2\left(3+\frac{49}{20}\right)$$

Multiply 3 and 2 to get 6.

$$\frac{187}{10}+28y=6\left(3+\frac{49}{20}\right)$$

Add 3 and \frac{49}{20} to get \frac{109}{20}.

$$\frac{187}{10}+28y=6\times \frac{109}{20}$$

Multiply 6 and \frac{109}{20} to get \frac{327}{10}.

$$\frac{187}{10}+28y=\frac{327}{10}$$

Subtract \frac{187}{10} from both sides.

$$28y=\frac{327}{10}-\frac{187}{10}$$

Subtract \frac{187}{10} from \frac{327}{10} to get 14.

$$28y=14$$

Divide both sides by 28.

$$y=\frac{14}{28}$$

Reduce the fraction \frac{14}{28} to lowest terms by extracting and canceling out 14.

$$y=\frac{1}{2}$$

The system is now solved.

$$x=\frac{49}{20} y=\frac{1}{2}$$