Consider the system of equations
ax^2 + by^3 = c
dx^2 + ey^3 = f
where a, b, c, d, e, and f are real constants and ae != bd. The maximum number of real solutions (x,y) of the system is:
The answer is two. Though I'm not sure how they got that. If you subtract one from the other you get (a-d)x^2 + (b-e)y^3 = c-f, which has at least 3 solutions, 2 for positive and negatives values of x when y is 0, and 1 for y when x is 0. What am I missing?