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Consider the following system of linear equations, where \(k \in \mathbb{R}\):$$\left\{\begin{array}{rcrcr} x & + & ky & = & 3 \\ 2x & + & 4y & = & 1\end{array}\right.$$Determine the values of \(k\) for which the system has:
  1. a unique solution.
  2. no solution.
  3. infinitely many solutions.
For the case where a unique solution exists, find the expressions for \(x\) and \(y\) in terms of \(k\).
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