Nonlinear Systems & Linearization · Superchallenge problem

A predator–prey system with both species harvested at per-capita rate $1$ is $x' = x(4 - 2y) - x,\; y' = y(3x - 6) - y$. Every positive solution other than the equilibrium is periodic. Over one full period of any such solution, find the time-average of the total population $x + y$.