Solve {l}{x/3+y/2+4=x+y+7/2}{2/5(x+2)=frac{2x+y}{10}+1}

$$\left. \begin{array}{l}{ \frac { x } { 3 } + \frac { y } { 2 } + 4 = \frac { x + y + 7 } { 2 } }\\{ \frac { 2 } { 5 } ( x + 2 ) = \frac { 2 x + y } { 10 } + 1 }\end{array} \right.$$

Solve for x, y

$$x=3$$

$$y=4$$

Solution Steps

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

$$2x+3y+24=3\left(x+y+7\right)$$

Use the distributive property to multiply 3 by x+y+7.

$$2x+3y+24=3x+3y+21$$

Subtract 3x from both sides.

$$2x+3y+24-3x=3y+21$$

Combine 2x and -3x to get -x.

$$-x+3y+24=3y+21$$

Subtract 3y from both sides.

$$-x+3y+24-3y=21$$

Combine 3y and -3y to get 0.

$$-x+24=21$$

Subtract 24 from both sides.

$$-x=21-24$$

Subtract 24 from 21 to get -3.

$$-x=-3$$

Divide both sides by -1.

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

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$x=3$$

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

$$\frac{2}{5}\left(3+2\right)=\frac{2\times 3+y}{10}+1$$

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

$$4\left(3+2\right)=2\times 3+y+10$$

Add 3 and 2 to get 5.

$$4\times 5=2\times 3+y+10$$

Multiply 4 and 5 to get 20.

$$20=2\times 3+y+10$$

Multiply 2 and 3 to get 6.

$$20=6+y+10$$

Add 6 and 10 to get 16.

$$20=16+y$$

Swap sides so that all variable terms are on the left hand side.

$$16+y=20$$

Subtract 16 from both sides.

$$y=20-16$$

Subtract 16 from 20 to get 4.

$$y=4$$

The system is now solved.

$$x=3 y=4$$