There are two species interacting: a prey species x and a predator species y. For the purposes of the model no other species interact with these two. In the absence of the predator, the prey exhibits pure exponential growth. There is enough food and resources to allow the prey to grow indefinitely. In the absence of prey, the predator dies out exponentially. This means that there is other food for the predator than the prey, but not enough to sustain the population. Thus, extinction takes years rather than days. When there are both predator and prey, the predators kill the prey such that the predator population increases at a rate proportional to the product of the number of predators and the number of prey. The prey population is decreased in a similar manner. Let y be the number of predator, and x be the number of prey. Our assumptions above lead us to write: dx/dt = ax - bxy, dy/dt = -cx + dxy, where a > 0 is the rate at which prey population increase when there are no predators, d > 0 is the rate at which the predators die out when there is no prey, b > 0 is the rate at which prey are killed off when there are predators present, and c > 0 is the rate and which predators population increases when there are prey. a. Find the equilibrium points for the system. b. Determine the Jacobian matrix of the system. c. Use the eigenvalue method to discuss the stability at each equilibrium point.