Solve xy+3y=x-5

$$x y + 3 y = x - 5$$

Solve for x

$$x=-\frac{3y+5}{y-1}$$

$$y\neq 1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xy+3y-x=-5$$

Subtract 3y from both sides.

$$xy-x=-5-3y$$

Combine all terms containing x.

$$\left(y-1\right)x=-5-3y$$

The equation is in standard form.

$$\left(y-1\right)x=-3y-5$$

Divide both sides by y-1.

$$\frac{\left(y-1\right)x}{y-1}=\frac{-3y-5}{y-1}$$

Dividing by y-1 undoes the multiplication by y-1.

$$x=\frac{-3y-5}{y-1}$$

Divide -5-3y by y-1.

$$x=-\frac{3y+5}{y-1}$$

Solve for y

$$y=-\frac{5-x}{x+3}$$

$$x\neq -3$$

Steps for Solving Linear Equation

Combine all terms containing y.

$$\left(x+3\right)y=x-5$$

Divide both sides by x+3.

$$\frac{\left(x+3\right)y}{x+3}=\frac{x-5}{x+3}$$

Dividing by x+3 undoes the multiplication by x+3.

$$y=\frac{x-5}{x+3}$$