$$\frac{dx}{dt}=4x-7y-1$$ $$\frac{dy}{dt}=3x+6y-12$$
one part of my notes says if the determinant gives you some number other than zero then there is only one equilibrium solution (the origin).
However another part of my notes says that the equilibrium solutions are just setting each equation to zero and solving for the variables. I think the determinant answer is the "more correct" one. Please shed some light on this. Thank you.