Solve y=3xy+x

$$y = 3 x y + x$$

Solve for x

$$x=\frac{y}{3y+1}$$

$$y\neq -\frac{1}{3}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$3xy+x=y$$

Combine all terms containing x.

$$\left(3y+1\right)x=y$$

Divide both sides by 3y+1.

$$\frac{\left(3y+1\right)x}{3y+1}=\frac{y}{3y+1}$$

Dividing by 3y+1 undoes the multiplication by 3y+1.

$$x=\frac{y}{3y+1}$$

Solve for y

$$y=\frac{x}{1-3x}$$

$$x\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Subtract 3xy from both sides.

$$y-3xy=x$$

Combine all terms containing y.

$$\left(1-3x\right)y=x$$

Divide both sides by 1-3x.

$$\frac{\left(1-3x\right)y}{1-3x}=\frac{x}{1-3x}$$

Dividing by 1-3x undoes the multiplication by 1-3x.

$$y=\frac{x}{1-3x}$$