@Axel Vogt My teacher will read it, so I'm looking for an "algorithm-like" method, rather than a graph.

@sursumCorda Thank you for your suggestion. I've found a command that is so close to my goal, that is HasRealRoot. What I want is to check if it has positive real root for both (x,y). Can we do something to modified the HasRealRoot command?

@dharr Thank you for your reply. I want to include the result in an article so perhaps "looking at" graph is not a good method (I guess sometimes, the roots may look too small to see!?). I'm thinking if we can find the intersection of the curve and the first quarter plane. Is there an algorithm to take some points of the curves created by the implicit plot and the first quarter plane? Like if Maple is able to plot the curves, then it has to calculate some points on the curves, "store" those points, and then draw the plot. Can we access the storage point? 

Sorry if I misunderstood some concepts as I'm not too familiar with CAS stuff.