Solve 2x+5y=2x{y}_{}

$$2x+5y = 2x { y }_{ }$$

Solve for x

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

$$y\neq 1$$

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$2x+5y-2xy=0$$

Subtract 5y from both sides. Anything subtracted from zero gives its negation.

$$2x-2xy=-5y$$

Combine all terms containing x.

$$\left(2-2y\right)x=-5y$$

Divide both sides by -2y+2.

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

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

$$x=-\frac{5y}{2-2y}$$

Divide -5y by -2y+2.

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

Solve for y

$$y=-\frac{2x}{5-2x}$$

$$x\neq \frac{5}{2}$$

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$2x+5y-2xy=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$5y-2xy=-2x$$

Combine all terms containing y.

$$\left(5-2x\right)y=-2x$$

Divide both sides by 5-2x.

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

Dividing by 5-2x undoes the multiplication by 5-2x.

$$y=-\frac{2x}{5-2x}$$