3. For which $a$ does the solution $(x, y, z)$ of the system $\left\{\begin{array}{c}3 x-y=a-2 \\ y+2 z=-a-1 \\ 3 x-2 z=2 a+3\end{array}\right.$ satisfy the equation $x^{2}+(y-2)^{2}+(z-1)^{2}=2$? Find these solutions.
Answer: 1) when $a=-3, x=-1, y=2, z=0$;

2) when $a=-\frac{51}{13}, x=-\frac{17}{13}, y=2, z=\frac{6}{13}$.