1. Find an equilibrium solution of the following system:
x' = 3x + 2y - 4
y' = x + 2y - 7
Solution
The system is in equilibrium if x ' = y ' = 0. So it reduces to
3x + 2y = 4 ---------1
x + 2y = 7. --------2
from 1
2y = 4-3x----------3

2. 3 in 2
x+4-3x =7
-2x = 7-4
x = -3/2
Plug this into either equation to get y.
2y = 4-3x
2y = 4 - 3(-3/2)
2y = -1/2
y = -1/4

3. y = -1/4 ,x = -3/2