Nonlinear Systems & Linearization · Challenge problem

Two species compete: $x' = x(3 - x - 2y),\; y' = y(2 - x - y)$. Both one-species states $(3, 0)$ and $(0, 2)$ are stable, and the coexistence equilibrium is a saddle whose stable manifold separates their basins. Find the slope of that separatrix at the saddle.