Solve kx-y+3k+2=0

$$k x - y + 3 k + 2 = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{2-y}{x+3}\text{, }&x\neq -3\\k\in \mathrm{C}\text{, }&y=2\text{ and }x=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add y to both sides. Anything plus zero gives itself.

$$kx+3k+2=y$$

Subtract 2 from both sides.

$$kx+3k=y-2$$

Combine all terms containing k.

$$\left(x+3\right)k=y-2$$

Divide both sides by x+3.

$$\frac{\left(x+3\right)k}{x+3}=\frac{y-2}{x+3}$$

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

$$k=\frac{y-2}{x+3}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y-3k-2}{k}\text{, }&k\neq 0\\x\in \mathrm{C}\text{, }&k=0\text{ and }y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Add y to both sides. Anything plus zero gives itself.

$$kx+3k+2=y$$

Subtract 3k from both sides.

$$kx+2=y-3k$$

Subtract 2 from both sides.

$$kx=y-3k-2$$

Divide both sides by k.

$$\frac{kx}{k}=\frac{y-3k-2}{k}$$

Dividing by k undoes the multiplication by k.

$$x=\frac{y-3k-2}{k}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{2-y}{x+3}\text{, }&x\neq -3\\k\in \mathrm{R}\text{, }&y=2\text{ and }x=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add y to both sides. Anything plus zero gives itself.

$$kx+3k+2=y$$

Subtract 2 from both sides.

$$kx+3k=y-2$$

Combine all terms containing k.

$$\left(x+3\right)k=y-2$$

Divide both sides by x+3.

$$\frac{\left(x+3\right)k}{x+3}=\frac{y-2}{x+3}$$

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

$$k=\frac{y-2}{x+3}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y-3k-2}{k}\text{, }&k\neq 0\\x\in \mathrm{R}\text{, }&k=0\text{ and }y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Add y to both sides. Anything plus zero gives itself.

$$kx+3k+2=y$$

Subtract 3k from both sides.

$$kx+2=y-3k$$

Subtract 2 from both sides.

$$kx=y-3k-2$$

Divide both sides by k.

$$\frac{kx}{k}=\frac{y-3k-2}{k}$$

Dividing by k undoes the multiplication by k.

$$x=\frac{y-3k-2}{k}$$