3. For which $a$ does the solution $(x, y, z)$ of the system $\left\{\begin{array}{l}2 x+3 y=a-1 \\ 3 y+4 z=a+1 \\ x+2 z=a-2\end{array}\right.$ satisfy the equation $(x+1)^{2}+y^{2}+(z+2)^{2}=\frac{49}{9}$? Find these solutions.
Answer: 1) when $a=-3, x=-3, y=\frac{2}{3}, z=-1$;

2) when $a=\frac{9}{5}, x=-\frac{3}{5}, y=\frac{2}{3}, z=\frac{1}{5}$.