Overview:
This interactive will help you identify the algebraic steps involved in calculations of this type.
From the Text:

QUESTION: Consider the non-linear system

x' = x(5 - x -y),
y' = -y(1 - x + y).

Try It Yourself:
Investigate this situation further with these new values.

x' = x(4 - x -y)
y' = -y(1 - x + 2y)