Question 4 Consider the following system i = ar - bry, y = -cy + dry, where a, b, c and d are strictly positive constants. (i) Show that the equilibrium points of the system are (0, 0) and (6, ;). (ii) Given L(x,y) = dx - elne + by - alny + K, where K is a constant. Verify that i =0 along the solutions of the dynamical system. (iii) Determine the value for K such that L(, -) = 0. (iv) Show that the equilibrium point (6, ;) is stable using L(x, y) with the value of K determined above