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Consider the following system of linear equations, where \(k \in \mathbb{R}\):$$\left\{\begin{array}{rcrcrcr} x &+& y &+& z &=& 3 \\ x &+& 2y &-& z &=& 4 \\ 2x &+& 3y &+& kz &=& 8\end{array}\right.$$
  1. Find the value of \(k\) for which the system does not have a unique solution.
  2. For this value of \(k\), determine if the system has no solution or infinitely many solutions.
  3. Describe the geometric interpretation of the system for this value of \(k\).
  4. Given that \(k=1\), find the unique solution to the system.

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