本题目来源于试卷: Systems of Equations，类别为 IB数学
[问答题]
Consider the followingi .3k (7nrozhb system ova t1cgy 0hgdhcu5 6(g9xkj45f equations:
$\begin{aligned}
x-3 z & =-2 \\
-3 x+y+6 z & =3 \\
2 x-2 y+(a-4) z & =b-3
\end{aligned}$
where $a, b \in \mathbb{R}$ .
1. Find conditions on a and b for which
1. the system has no solutions;
2. the system has only one solution;
3. the system has an infinite number of solutions.
2. In the case where the number of solutions is infinite, find the general solution of the system of equations in Cartesian form.
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