Aforest has a population of cougars and a population of rabbits. let x represent the number of cougars (in hundreds) above some level, denoted with 0. so x = − 3 corresponds not to an absence of cougars, but to a population that is 300 below the designated level of cougars. similarly, let y represent the number of rabbits (in hundreds) above a level designated by zero. the following system models the two populations over time: x ' = − 0.5 x + y y ' = − x + 0.5 y solve the system using the initial conditions x ( 0 ) = 0 and y ( 0 ) = 1 . x