Chapter 1.1, Problem 22E

In the following predator-prey population models,x represents the prey, and y represents the predators.
(i) $\begin{array}{l}\frac{dx}{dt}=5x-3xy\\ \frac{dy}{dt}=-2y+\frac{1}{2}xy\end{array}$     (ii) $\begin{array}{l}\frac{dx}{dt}=x-8xy\\ \frac{dy}{dt}=-2y+6xy\end{array}$
(a) In which system does the prey reproduce more quickly when there are no predators (when y = 0) and equal numbers of prey?
(b) In which system are the predators more successful at catching prey? In other words, if the number of predators and prey are equal for the two systems, in which system do the predators have a greater effect on the rate of change of the prey?
(c) Which system requires more prey for the predators to achieve a given growth rate (assuming identical numbers of predators in both cases)?