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Consider the following system of linear equations, where \(k \in \mathbb{R}\):$$\left\{\begin{array}{rcrcr} 2x & - & y & = & 4 \\ -6x & + & 3y & = & k\end{array}\right.$$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 infinitely many solutions exist, find the general solution in parametric form.
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