10 Find the set of values of \(a\) for which the system of equations
$$\begin{aligned}
x - 2 y - 2 z & = - 7
2 x + ( a - 9 ) y - 10 z & = - 11
3 x - 6 y + 2 a z & = - 29
\end{aligned}$$
has a unique solution.
Show that the system has no solution in the case \(a = - 3\).
Given that \(a = 5\),
- show that the number of solutions is infinite,
- find the solution for which \(x + y + z = 2\).