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

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

Solve for x

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

$$y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

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

$$yx-y+x\left(y-1\right)=1-y$$

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

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

Combine yx and xy to get 2yx.

$$2yx-y-x=1-y$$

Add y to both sides.

$$2yx-x=1-y+y$$

Combine -y and y to get 0.

$$2yx-x=1$$

Combine all terms containing x.

$$\left(2y-1\right)x=1$$

Divide both sides by 2y-1.

$$\frac{\left(2y-1\right)x}{2y-1}=\frac{1}{2y-1}$$

Dividing by 2y-1 undoes the multiplication by 2y-1.

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

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$yx-y+x\left(y-1\right)=1-y$$

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

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

Combine yx and xy to get 2yx.

$$2yx-y-x=1-y$$

Add y to both sides.

$$2yx-y-x+y=1$$

Combine -y and y to get 0.

$$2yx-x=1$$

Add x to both sides.

$$2yx=1+x$$

The equation is in standard form.

$$2xy=x+1$$

Divide both sides by 2x.

$$\frac{2xy}{2x}=\frac{x+1}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

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

Divide x+1 by 2x.

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