Differential Equations on Population

Question

I've been beginning to try to solve some simple differential equations. I reached a problem where there is a polar bear population $p(t)$ and a seal population $s(t)$ that are governed by $$\frac{dp}{dt} = p(t) - 3s(t)$$ $$\frac{ds}{dt} = 2p(t) + 4s(t)$$ Assuming a continuous approximation of population. I'm interested in solving for the asymptotic behavior of the populations of polar bears and seals. I was wondering, what would the asymptotic behavior of this function be like if $p(0) = 3000$ and $s(0) = 5000$? If so, is there a good way to solve this using some linear system of equations?