25-14 On the $x O y$ plane, the number of distinct common points of the figures: $(x+y-5)(2x-3y+5)=0$ and $(x-y+1)(3x+2y-12)=0$ is
(A) 0.
(B) 1.
(C) 2.
(D) 3.
(E) 4.
(G) Infinite.
(21st American High School Mathematics Examination, 1970)
［Solution］The two equations are equivalent to the following four linear equations:
$$
\begin{array}{ll}
\text { I }: x+y-5=0, & \text { II }: 2 x-3 y+5=0, \\
\text { III: } x-y+1=0, & \text { IV }: 3 x+2 y-12=0 .
\end{array}
$$

It is easy to verify that all four lines pass through the point $(2,3)$.
Since these lines have different slopes, they have only one common point. Therefore, the answer is $(B)$.