I have a rather sloppy proof . . .
True or False?
Every system of two conic equations whose xy-term is nonexistent
has at most 4 points of intersection. . . True!
We have two conic equations: .
Solve  for
. . Quadratic Formula: .
Substitute into :
. . .
This simplifies to a quartic in . . . which has at most 4 roots.