How many possible solutions are there to a system of equations that include conic sections

Thanks.

It depends. If you think about it geometrically, the equation of a conic section is really just an algebraic representation of that shape (circle, ellipse, hyperbola, parabola). To solve a system of equations, you are looking for where the graphs intersect. So, if you pair a linear equation with a conic section for example, you get 2 possible solutions (a line could intersect a circle twice at most). If you have 2 conic sections like say a parabola and a circle, you can have more intersections (4 in that case).

The fuq did I jus read?