Solve 2xy+x+y=83

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

Solve for x

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

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

Steps for Solving Linear Equation

Subtract y from both sides.

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

Combine all terms containing x.

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

Divide both sides by 2y+1.

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

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

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

Solve for y

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

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

Steps for Solving Linear Equation

Subtract x from both sides.

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

Combine all terms containing y.

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

Divide both sides by 2x+1.

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

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

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