$[$Solve by hand$-$writing$]$

The following system of ODEs is given.

$\frac{dx}{dt}=24x-2x^2-3xY$

$\frac{dY}{dt}=15Y-Y^2-3xY$

$($a$)$ Identify equilibrium point$($s$).$

$($b$)$ Use slope analysis to analyze the stability of the identified equilibrium points and draw an approximate phase plane.

$($c$)$ Use the eigenvalue approach to analyze the stability of the identified equilibrium points.