Solve xy+6y=1

$$x y + 6 y = 1$$

Solve for x

$$x=-6+\frac{1}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract 6y from both sides.

$$xy=1-6y$$

The equation is in standard form.

$$yx=1-6y$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{1-6y}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{1-6y}{y}$$

Divide 1-6y by y.

$$x=-6+\frac{1}{y}$$

Solve for y

$$y=\frac{1}{x+6}$$

$$x\neq -6$$

Steps for Solving Linear Equation

Combine all terms containing y.

$$\left(x+6\right)y=1$$

Divide both sides by x+6.

$$\frac{\left(x+6\right)y}{x+6}=\frac{1}{x+6}$$

Dividing by x+6 undoes the multiplication by x+6.

$$y=\frac{1}{x+6}$$