Solve (x+1)(y-1)=xy+2017

$$( x + 1 ) ( y - 1 ) = x y + 2017$$

Solve for x

$$x=y-2018$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by y-1.

$$xy-x+y-1=xy+2017$$

Subtract xy from both sides.

$$xy-x+y-1-xy=2017$$

Combine xy and -xy to get 0.

$$-x+y-1=2017$$

Subtract y from both sides.

$$-x-1=2017-y$$

Add 1 to both sides.

$$-x=2017-y+1$$

Add 2017 and 1 to get 2018.

$$-x=2018-y$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{2018-y}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{2018-y}{-1}$$

Divide 2018-y by -1.

$$x=y-2018$$

Solve for y

$$y=x+2018$$

Solution Steps

Use the distributive property to multiply x+1 by y-1.

$$xy-x+y-1=xy+2017$$

Subtract xy from both sides.

$$xy-x+y-1-xy=2017$$

Combine xy and -xy to get 0.

$$-x+y-1=2017$$

Add x to both sides.

$$y-1=2017+x$$

Add 1 to both sides.

$$y=2017+x+1$$

Add 2017 and 1 to get 2018.

$$y=2018+x$$