Solve (2x+2)(2y-3)-(x-2)(4y+2)=2

$$(2x+2)(2y-3)-(x-2)(4y+2)=2$$

Solve for x

$$x=\frac{3y-1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+2 by 2y-3.

$$4xy-6x+4y-6-\left(x-2\right)\left(4y+2\right)=2$$

Use the distributive property to multiply x-2 by 4y+2.

$$4xy-6x+4y-6-\left(4xy+2x-8y-4\right)=2$$

To find the opposite of 4xy+2x-8y-4, find the opposite of each term.

$$4xy-6x+4y-6-4xy-2x+8y+4=2$$

Combine 4xy and -4xy to get 0.

$$-6x+4y-6-2x+8y+4=2$$

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

$$-8x+4y-6+8y+4=2$$

Combine 4y and 8y to get 12y.

$$-8x+12y-6+4=2$$

Add -6 and 4 to get -2.

$$-8x+12y-2=2$$

Subtract 12y from both sides.

$$-8x-2=2-12y$$

Add 2 to both sides.

$$-8x=2-12y+2$$

Add 2 and 2 to get 4.

$$-8x=4-12y$$

Divide both sides by -8.

$$\frac{-8x}{-8}=\frac{4-12y}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x=\frac{4-12y}{-8}$$

Divide 4-12y by -8.

$$x=\frac{3y-1}{2}$$

Solve for y

$$y=\frac{2x+1}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+2 by 2y-3.

$$4xy-6x+4y-6-\left(x-2\right)\left(4y+2\right)=2$$

Use the distributive property to multiply x-2 by 4y+2.

$$4xy-6x+4y-6-\left(4xy+2x-8y-4\right)=2$$

To find the opposite of 4xy+2x-8y-4, find the opposite of each term.

$$4xy-6x+4y-6-4xy-2x+8y+4=2$$

Combine 4xy and -4xy to get 0.

$$-6x+4y-6-2x+8y+4=2$$

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

$$-8x+4y-6+8y+4=2$$

Combine 4y and 8y to get 12y.

$$-8x+12y-6+4=2$$

Add -6 and 4 to get -2.

$$-8x+12y-2=2$$

Add 8x to both sides.

$$12y-2=2+8x$$

Add 2 to both sides.

$$12y=2+8x+2$$

Add 2 and 2 to get 4.

$$12y=4+8x$$

The equation is in standard form.

$$12y=8x+4$$

Divide both sides by 12.

$$\frac{12y}{12}=\frac{8x+4}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$y=\frac{8x+4}{12}$$

Divide 4+8x by 12.

$$y=\frac{2x+1}{3}$$