Chapter 3.6, Problem 25P

A model for the population, $x$ and $y$ of two species, that compete for the same food supply is $\frac{dx}{dt}=x\left(1-x-y\right),\frac{dy}{dt}=y\left(0.75-y-0.5x\right)$. Find all the critical points of the system, draw a direction field and phase portrait and interpret the meaning of the limiting behaviour as $t\to \infty$ $x$ and $y$ in terms of the population of the two species.