Solve x*(y-2)+1-y=0=

$$x \times (y-2)+1-y=0=$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

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

$$xy-2x+1-y=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$xy-2x-y=-1$$

Add y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-2.

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

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

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

$$xy-2x+1-y=0$$

Add 2x to both sides. Anything plus zero gives itself.

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

Subtract 1 from both sides.

$$xy-y=2x-1$$

Combine all terms containing y.

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

Divide both sides by x-1.

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

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

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