Solve 2xy+2x-y=10

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

Solve for x

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

$$y\neq -1$$

Steps for Solving Linear Equation

Add y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2y+2.

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

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

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

Divide y+10 by 2y+2.

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

Solve for y

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

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

Steps for Solving Linear Equation

Subtract 2x from both sides.

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

Combine all terms containing y.

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

Divide both sides by 2x-1.

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

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

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

Divide 10-2x by 2x-1.

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