(e) If \(x=0\)what happens to \(y\left(t\right)\)? How is this indicated in the phase-plane? If \(y=0\), what happens to \(x\left(t\right)\)? How is this indicated in the phase-plane?
Answer: 
As \(x=0\)\(\frac{dy}{dt}\) increases, which means that \(y\) increases.
As \(y=0\)\(\frac{dx}{dt}\) increases, which means that \(x\) increases.
(g) For each of the initial conditions given below, describe how the number of species of and change with time and what the situations will look like in the long run.
i) \(x(0)=2\ and\ y(0)=1.8\)
Answer:  Population of A will increase over time and the population of will decrease since it is a competitive environment. In the long run, the population of B would tend to zero.
ii) \(x(0)=2\ and\ y(0)=2.3\)
Answer:  Population of A will decrease over time and the population of will increase since it is a competitive environment. In the long run, the population of A would tend to zero.
iii) \(x(0)=2.2\ and\ y(0)=2\ \)
Answer:  Population of B will decrease over time and the population of will increase since it is a competitive environment. In the long run, the population of B would tend to zero.

Question 3