4. The number of positive integer solutions to the system of equations $\left\{\begin{array}{l}x y+y z=63, \\ x z+y z=23\end{array}\right.$ is ).
(A) 1
(B) 2
(C) 3
(D) 4
4.  April From the second equation, we have $(x+y) z=23$. Since $x+y \geqslant 2$ and 23 is a prime number, it follows that $z=1, x+y=23$. Substituting $z=1, y=23-x$ into the first equation, we get $x^{2}-22 x+40=0$. The two roots of the equation are $x_{1}=2, x_{2}=20$. Solving this, we find that the system of equations has two sets of integer solutions.