7 Three planes have equations,
$$\begin{gathered}
x - y + k z = 3
k x - 3 y + 5 z = - 1
x - 2 y + 3 z = - 4
\end{gathered}$$
Where \(k\) is a real constant. The planes do not meet at a unique point.
7
- Find the possible values of \(k\)
7
- There are two possible geometric configurations of the given planes.
Identify each possible configurations, stating the corresponding value of \(k\)
Fully justify your answer.
[0pt]
[5 marks]
7 - Given further that the equations of the planes form a consistent system, find the solution of the system of equations.