Solve 5xy=x-5y

$$5 x y = x - 5 y$$

Solve for x

$$x=-\frac{5y}{5y-1}$$

$$y\neq \frac{1}{5}$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

Combine all terms containing x.

$$\left(5y-1\right)x=-5y$$

Divide both sides by 5y-1.

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

Dividing by 5y-1 undoes the multiplication by 5y-1.

$$x=-\frac{5y}{5y-1}$$

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Add 5y to both sides.

$$5xy+5y=x$$

Combine all terms containing y.

$$\left(5x+5\right)y=x$$

Divide both sides by 5x+5.

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

Dividing by 5x+5 undoes the multiplication by 5x+5.

$$y=\frac{x}{5x+5}$$

Divide x by 5x+5.

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