Solve (x+y)-(9x-11x)=2y-2

$$( x + y ) - ( 9 x - 11 x ) = 2 y - 2$$

Solve for x

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

Steps for Solving Linear Equation

Combine 9x and -11x to get -2x.

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

The opposite of -2x is 2x.

$$x+y+2x=2y-2$$

Combine x and 2x to get 3x.

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

Subtract y from both sides.

$$3x=2y-2-y$$

Combine 2y and -y to get y.

$$3x=y-2$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Solve for y

$$y=3x+2$$

Steps for Solving Linear Equation

Combine 9x and -11x to get -2x.

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

The opposite of -2x is 2x.

$$x+y+2x=2y-2$$

Combine x and 2x to get 3x.

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

Subtract 2y from both sides.

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

Combine y and -2y to get -y.

$$3x-y=-2$$

Subtract 3x from both sides.

$$-y=-2-3x$$

The equation is in standard form.

$$-y=-3x-2$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -2-3x by -1.

$$y=3x+2$$