Solve 2xy+y-2x=10

$$2 x y + y - 2 x = 10$$

Solve for x

$$x=-\frac{y-10}{2\left(y-1\right)}$$

$$y\neq 1$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$2xy-2x=10-y$$

Combine all terms containing x.

$$\left(2y-2\right)x=10-y$$

Divide both sides by 2y-2.

$$\frac{\left(2y-2\right)x}{2y-2}=\frac{10-y}{2y-2}$$

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

$$x=\frac{10-y}{2y-2}$$

Divide 10-y by 2y-2.

$$x=\frac{10-y}{2\left(y-1\right)}$$

Solve for y

$$y=\frac{2\left(x+5\right)}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Add 2x to both sides.

$$2xy+y=10+2x$$

Combine all terms containing y.

$$\left(2x+1\right)y=10+2x$$

The equation is in standard form.

$$\left(2x+1\right)y=2x+10$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)y}{2x+1}=\frac{2x+10}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$y=\frac{2x+10}{2x+1}$$

Divide 10+2x by 2x+1.

$$y=\frac{2\left(x+5\right)}{2x+1}$$