4. The number of intersection points of the curves $2 x^{2}-x y-y^{2}-x-2 y-1=0$ and $3 x^{2}-$ $4 x y+y^{2}-3 x+y=0$ is ( ).
(A) 2
(B) 3
(C) 4
(D) infinitely many
4.D.
$2 x^{2}-x y-y^{2}-x-2 y-1=0$, i.e.,
$2 x+y+1=0$ or $x-y-1=0$.
$3 x^{2}-4 x y+y^{2}-3 x+y=0$, i.e.,
$3 x-y=0$ or $x-y-1=0$.
Therefore, both curves can degenerate into two lines, and one pair of lines coincide. Hence, the two curves have infinitely many common points.