Suppose I have two equations:
$$\frac{dx}{dt} = x(2-x-y),\,
\frac{dy}{dt} = ky(2-ax-by)$$
that together form a 2D ODE system ($x$ plotted against $y). K, a$ and $b$ are all independent positive parameters. However, I am only interested in points at the line where $y = 3 \text{(or some other constant)} - x,\, $ as I am simulating a field that is always fully occupied by both $x$ and $y$ with no empty spaces. Is there a possibility to reduce the whole system to only this line, e.g. make the 2D system into a 1D line that is a good representation of the system in 2D at this line?