Solve xy-2(x-1)=4y

$$x y - 2 ( x - 1 ) = 4 y$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$xy-2x+2=4y$$

Subtract 2 from both sides.

$$xy-2x=4y-2$$

Combine all terms containing x.

$$\left(y-2\right)x=4y-2$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{4y-2}{y-2}$$

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

$$x=\frac{4y-2}{y-2}$$

Divide 4y-2 by y-2.

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

Solve for y

$$y=-\frac{2\left(1-x\right)}{x-4}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$xy-2x+2=4y$$

Subtract 4y from both sides.

$$xy-2x+2-4y=0$$

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

$$xy+2-4y=2x$$

Subtract 2 from both sides.

$$xy-4y=2x-2$$

Combine all terms containing y.

$$\left(x-4\right)y=2x-2$$

Divide both sides by x-4.

$$\frac{\left(x-4\right)y}{x-4}=\frac{2x-2}{x-4}$$

Dividing by x-4 undoes the multiplication by x-4.

$$y=\frac{2x-2}{x-4}$$

Divide -2+2x by x-4.

$$y=\frac{2\left(x-1\right)}{x-4}$$