A previous exercise modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: $$\begin{aligned} \frac{dA}{dt} &= 1 A(1 - 0.0005 A) - 0.03 AL \\ \frac{dL}{dt} &= -0.4 L + 0.0004 AL \end{aligned}$$

(a). Find the equilibrium solutions.
Enter your answer as a list of ordered pairs $(A,L)$, where $A$ is the number of aphids and $L$ the number of ladybugs. For example, if you found three equilibrium solutions, one with 100 aphids and 10 ladybugs, one with 200 aphids and 20 ladybugs, and one with 300 aphids and 30 ladybugs, you would enter $(100,10),(200,20),(300,30)$. Do not round fractional answers to the nearest integer.
Answer =

(b). Find an expression for $dL/dA$.
$\displaystyle \frac{dL}{dA} =$