$\displaystyle \frac{dS}{dt} = \frac{K_{cat}E_{0}S}{K_{m} + S} $

$\displaystyle \frac{dP}{dt} = \frac{K_{cat}E_{0}S}{K_{m}+S} $

with intial conditions $\displaystyle S(0) = S_{0} $ $\displaystyle P(0) = p_{0) $

show that S and P satisfy a conservation law given by S+P = c,

for some constant c, and find the value of c. Hence determine $\displaystyle \lim_{t\ \infty} P(t) $

I know that if you add the two equations you get a 0, is that what c equals?