Solve kx-y=k+3

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

Solve for k

$$\left\{\begin{matrix}k=\frac{y+3}{x-1}\text{, }&x\neq 1\\k\in \mathrm{R}\text{, }&y=-3\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract k from both sides.

$$kx-y-k=3$$

Add y to both sides.

$$kx-k=3+y$$

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by x-1.

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

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

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

Solve for x

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

Steps for Solving Linear Equation

Add y to both sides.

$$kx=k+3+y$$

The equation is in standard form.

$$kx=y+k+3$$

Divide both sides by k.

$$\frac{kx}{k}=\frac{y+k+3}{k}$$

Dividing by k undoes the multiplication by k.

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