2. B. Given that $x, y, z$ are real numbers, and satisfy
$$
x+2 y-5 z=3, x-2 y-z=-5 \text {. }
$$

Then the minimum value of $x^{2}+y^{2}+z^{2}$ is ().
(A) $\frac{1}{11}$
(B) 0
(C) 5
(D) $\frac{54}{11}$
2. B. D.

From the given, we have $\left\{\begin{array}{l}x=3 z-1 \\ y=z+2\end{array}\right.$, thus, $x^{2}+y^{2}+z^{2}=11 z^{2}-2 z+5$. Therefore, when $z=\frac{1}{11}$, the minimum value of $x^{2}+y^{2}+z^{2}$ is $\frac{54}{11}$.