$$\left. \begin{array} { l } { \quad y = \frac { c } { x } + 2 } \end{array} \right.$$
$\left\{\begin{matrix}x=-\frac{c}{2-y}\text{, }&c\neq 0\text{ and }y\neq 2\\x\neq 0\text{, }&y=2\text{ and }c=0\end{matrix}\right.$
$$yx=c+x\times 2$$
$$yx-x\times 2=c$$
$$yx-2x=c$$
$$\left(y-2\right)x=c$$
$$\frac{\left(y-2\right)x}{y-2}=\frac{c}{y-2}$$
$$x=\frac{c}{y-2}$$
$$x=\frac{c}{y-2}\text{, }x\neq 0$$
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