2. The indeterminate equation $96 x_{1}+97 x_{2}=1000$ has $(\quad)$ sets of non-negative integer solutions.
A. 0
B. 1
C. 2
D. 3
2. A The complete set of integer solutions for the equation can be obtained as
$$\left\{\begin{array}{l}
x=-30+97 t, \\
y=40-96 t
\end{array} \quad(t \in \mathbf{Z})\right.$$

Let $x, y \geqslant 0$, we get $\frac{30}{97} \leqslant t \leqslant \frac{40}{96}$, and $t$ has no integer values. Therefore, the equation has no non-negative integer solutions.