3. For which $a$ does the solution $(x, y, z)$ of the system $\left\{\begin{array}{l}x-2 y=a-1 \\ 2 z-y=a+2 \\ x+4 z=a+3\end{array}\right.$ satisfy the equation $(x+1)^{2}+y^{2}+(z-1)^{2}=20$ ? Find these solutions.
Answer: 1) when $a=8, x=-1, y=-4, z=3$;

2) when $a=-8, x=-1, y=4, z=-1$.