AHSME 1970 Problem 26

The number of distinct points in the $xy$-plane common to the graphs of $(x+y-5)(2x-3y+5)=0$ and $(x-y+1)(3x+2y-12)=0$ is $\text{(A) } 0 \text{(B) } 1 \text{(C) } 2 \text{(D) } 3 \text{(E) } 4 \text{(F) } \infty$