3. The number of integer solution sets for the system of equations $\left\{\begin{array}{l}x^{2}+x y+x z=10 \\ y z+y^{2}=15\end{array}\right.$ is ( ).
(A) 2 sets
(B) 4 sets
(C) More than 5 sets
(D) None of the above answers
3.(B).

Obviously, $y(y+z)=15$. Therefore, as long as $y+z \mid 15$, $y$ is an integer, then $z$ is also an integer. Given $x(x+y+z)=10$ ($x$ is an integer), after verification, it is found that only when $x=2, x=5, x=-2, x=-5$, $y+z \mid 15$. Hence, there are 4 pairs of $(y, z)$ corresponding to the four solutions of $x$.