Solve x+y+2xy=83

$$x+y+2xy=83$$

Solve for x

$$x=-\frac{y-83}{2y+1}$$

$$y\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$x+2xy=83-y$$

Combine all terms containing x.

$$\left(1+2y\right)x=83-y$$

The equation is in standard form.

$$\left(2y+1\right)x=83-y$$

Divide both sides by 1+2y.

$$\frac{\left(2y+1\right)x}{2y+1}=\frac{83-y}{2y+1}$$

Dividing by 1+2y undoes the multiplication by 1+2y.

$$x=\frac{83-y}{2y+1}$$

Solve for y

$$y=-\frac{x-83}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$y+2xy=83-x$$

Combine all terms containing y.

$$\left(1+2x\right)y=83-x$$

The equation is in standard form.

$$\left(2x+1\right)y=83-x$$

Divide both sides by 1+2x.

$$\frac{\left(2x+1\right)y}{2x+1}=\frac{83-x}{2x+1}$$

Dividing by 1+2x undoes the multiplication by 1+2x.

$$y=\frac{83-x}{2x+1}$$