Solve (x-1)(y+1)=17

$$( x - 1 ) ( y + 1 ) = 17$$

Solve for x

$$x=\frac{y+18}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

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

$$xy+x-y-1=17$$

Add y to both sides.

$$xy+x-1=17+y$$

Add 1 to both sides.

$$xy+x=17+y+1$$

Add 17 and 1 to get 18.

$$xy+x=18+y$$

Combine all terms containing x.

$$\left(y+1\right)x=18+y$$

The equation is in standard form.

$$\left(y+1\right)x=y+18$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{y+18}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=\frac{y+18}{y+1}$$

Solve for y

$$y=-\frac{x-18}{x-1}$$

$$x\neq 1$$

Steps for Solving Linear Equation

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

$$xy+x-y-1=17$$

Subtract x from both sides.

$$xy-y-1=17-x$$

Add 1 to both sides.

$$xy-y=17-x+1$$

Add 17 and 1 to get 18.

$$xy-y=18-x$$

Combine all terms containing y.

$$\left(x-1\right)y=18-x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)y}{x-1}=\frac{18-x}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$y=\frac{18-x}{x-1}$$