本题目来源于试卷: Systems of Equations，类别为 IB数学
[问答题]
Consider the followinln8m-ri 7dc3io0bp ce4oq7 ee+ep;, ictc, r(g sy2s bvpz zt8.hdgwh2+6 stem of equations:
$\begin{aligned}
x+y+4 z & =1 \\
3 x+2 y+16 z & =5 \\
4 x+2 y+(a-1) z & =b-4
\end{aligned}$
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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