$31 \cdot 23$ If $x=9, y=-4$ is a set of integer solutions to the binary quadratic equation $2 x^{2}+5 x y+3 y^{2}=30$, the number of different integer solutions to this equation is
(A) 2 sets.
(B) 6 sets.
(C) 12 sets.
(D) 16 sets.
(11th "Hope Cup" National Mathematics Invitational Competition, 1990)
［Solution］From the given, we have $(2 x+3 y)(x+y)=30$, thus
$$
\left\{\begin{aligned}
x+y & = \pm 1, \pm 2, \pm 3, \pm 5 ; \pm 30, \pm 15, \pm 10, \pm 6 ; \\
2 x+3 y & = \pm 30, \pm 15, \pm 10, \pm 6 ; \pm 1, \pm 2, \pm 3, \pm 5 .
\end{aligned}\right.
$$

A total of 16 different integer solutions can be obtained (note that the right side of the equation system takes the same sign).
Therefore, the answer is $(D)$.