A scientist places two strains of bacteria, X and Y, in a petri dish. Initially, there are 400 of X and 500 of Y. The two bacteria compete for food and space but do not feed on each other. If x = x(t) and y = y(t) are the numbers of the strains at time t days, the growth rates of the two populations are given by the system
x′ = 1.2x - 0.2y
y′ = -0.2x + 1.5y

(a) Determine what happens to these two populations by solving the system of differential equations.
(b) Explore the effect of changing the initial populations by letting x(0) = a and y(0) = b. Describe what happens to the populations in terms of a and b.