Consider the system of equations dx | dt = = x(3 - x - 4y) dy dt = y(1 - 3x), taking (x, y) > 0. Recall that a nullcline of this system is a line on which t dy = = 0. Likewise, a vertical nullcline of this dt dx dy system is a line on which = 0, and a horizontal nullcline of this system is a line on which = 0. dt dt (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=(3-X)/4 (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: y=0 (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria = (0,0),(3,0), (1/3,2/3) (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (1/3, 1), trajectories converge to the point (-4/9,0) (Enter the point as an (x,y) pair, e.g., (1,2).)