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 \(a=5\),
(i) show that the number of solutions is infinite,

(ii) find the solution for which \(x+y+z=2\).