Find all equilibrium points - if both populations are

Question

Question

When two species, such as the rhinoceros and birds, coexist in a symbiotic relationship, they either increase together or decrease together. Typical equations for the growth rates of two such species might be:

dx₁/dt = -4x₁ + 4x₁x₂

dx₂/dt = -3x₂  + 2x₁x₂

a. Find an equation relating x₁ and x₂ if x₁ = 5 when x₂ =1.

b. Find all equilibrium points.

c. If both populations are greater than their values at the equilibrium point, what happens to the populations?

d. If both populations are less than their values at the equilibrium point, what happens to the populations?