Let X be a recurrent point of a planar system, that is, there is a sequence tn →±[infinity] such that φtn (X) → X. (a) Prove that either X is an equilibrium or X lies on a closed orbit. (b) Show by example that there can be a recurrent point for a nonplanar system that is not an equilibrium and does not lie on a closed orbit.

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graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

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step-by-step explanation: