Predator-prey models are commonly applied to ecological systems where there are two dominant species, one of which acts as herbivorous prey and the other as a carnivorous predator. Predator-prey systems have been studied for decades and are known to exhibit interesting dynamics. In this case, the system being modeled is the interaction of snowshoe hares and Canadian lynx. The model is given as follows: H˙ (t) = (100 − L(t))H(t) (9) L˙(t) = (0.2H(t) − 50)L(t) − f(t) (10) where t is time in years, H is the hare population size, L is the lynx population size, and f represents the control input used by conservation ecologists to control the lynx population in order to ensure the health of the overall ecological system. (a) (3 points) What will be the population of hares and lynx in the equilibrium with no input? i. e., with f = 0, find out all possible equilibrium points (He, Le) for this nonlinear system.