I'm suppose to find equilibrium solutions that satisfy the following system of differential equations:
$$\frac{dx}{dt} = -3x+2y$$ $$\frac{dy}{dt} = 6x+y$$
This may be a simple question, but I feel like my instructor didn't explain how to go about this. All I know, if I'm even correct, is that we need to make sure that $\frac{dx}{dt} = 0$ and $\frac{dy}{dt} = 0$. I am not interested in a linear algebra approach for this problem. I'm just looking for a simple explanation as to how to approach problems similar to the one I asked.