Solve 3(x+y)+2(x-y)+3(x+y)-2(x-y)=6

$$3 ( x + y ) + 2 ( x - y ) + 3 ( x + y ) - 2 ( x - y ) = 6$$

Solve for x

$$x=1-y$$

Steps for Solving Linear Equation

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

$$3x+3y+2\left(x-y\right)+3\left(x+y\right)-2\left(x-y\right)=6$$

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

$$3x+3y+2x-2y+3\left(x+y\right)-2\left(x-y\right)=6$$

Combine 3x and 2x to get 5x.

$$5x+3y-2y+3\left(x+y\right)-2\left(x-y\right)=6$$

Combine 3y and -2y to get y.

$$5x+y+3\left(x+y\right)-2\left(x-y\right)=6$$

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

$$5x+y+3x+3y-2\left(x-y\right)=6$$

Combine 5x and 3x to get 8x.

$$8x+y+3y-2\left(x-y\right)=6$$

Combine y and 3y to get 4y.

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

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

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

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

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

Combine 4y and 2y to get 6y.

$$6x+6y=6$$

Subtract 6y from both sides.

$$6x=6-6y$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{6-6y}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{6-6y}{6}$$

Divide 6-6y by 6.

$$x=1-y$$

Solve for y

$$y=1-x$$

Steps for Solving Linear Equation

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

$$3x+3y+2\left(x-y\right)+3\left(x+y\right)-2\left(x-y\right)=6$$

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

$$3x+3y+2x-2y+3\left(x+y\right)-2\left(x-y\right)=6$$

Combine 3x and 2x to get 5x.

$$5x+3y-2y+3\left(x+y\right)-2\left(x-y\right)=6$$

Combine 3y and -2y to get y.

$$5x+y+3\left(x+y\right)-2\left(x-y\right)=6$$

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

$$5x+y+3x+3y-2\left(x-y\right)=6$$

Combine 5x and 3x to get 8x.

$$8x+y+3y-2\left(x-y\right)=6$$

Combine y and 3y to get 4y.

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

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

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

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

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

Combine 4y and 2y to get 6y.

$$6x+6y=6$$

Subtract 6x from both sides.

$$6y=6-6x$$

Divide both sides by 6.

$$\frac{6y}{6}=\frac{6-6x}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$y=\frac{6-6x}{6}$$

Divide 6-6x by 6.

$$y=1-x$$