Solve xy-5y=1

$$x y - 5 y = 1$$

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Add 5y to both sides.

$$xy=1+5y$$

The equation is in standard form.

$$yx=5y+1$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{5y+1}{y}$$

Dividing by y undoes the multiplication by y.

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

Divide 1+5y by y.

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

Solve for y

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

$$x\neq 5$$

Steps for Solving Linear Equation

Combine all terms containing y.

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

Divide both sides by x-5.

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

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

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