Find the set of values of \(k\) for which the system of equations
$$\begin{aligned}
x + 2 y + 3 z & = 1
k x + 4 y + 6 z & = 0
7 x + 8 y + 9 z & = 3
\end{aligned}$$
has a unique solution.
Interpret the situation geometrically in the case where the system of equations does not have a unique solution.