Solve xy+3y=k

$$x y + 3 y = k$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{k}{y}-3\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$xy=k-3y$$

The equation is in standard form.

$$yx=k-3y$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{k-3y}{y}$$

Dividing by y undoes the multiplication by y.

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

Divide k-3y by y.

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

Solve for x

$$\left\{\begin{matrix}x=\frac{k}{y}-3\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$xy=k-3y$$

The equation is in standard form.

$$yx=k-3y$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{k-3y}{y}$$

Dividing by y undoes the multiplication by y.

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

Divide k-3y by y.

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

Solve for k

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

Solution Steps

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

$$k=xy+3y$$