2010011206

Consider the system $$\begin{array}{rlrl}y& =\frac{k}{x},& & \\ y& =a,& & \end{array}$$ where $a$, $k$ are real parameters and $x$, $y$ are real variables. Determine the conditions for $a$ and $k$ so that the system has a unique solution in ${\mathbb{R}}^{+}\times {\mathbb{R}}^{-}$.