Differential equations systems

Question

We have that system of differential equations: $$ \left\{ \begin{array}{ll} x'=-x \\ y'=-2y \\ \end{array} \right. $$ I have to solve that system but I only know the method of derive first equation and substitute in the second and get a second order differential equation which I know to solve. But it seems that that method doesn't work here. How can I solve it? I'm beginner at this kind of exercises. Thanks!

Answer 1

These are two unrelated DE's and you have to solve them independently. The answer is $x(t)=ce^{-t}$ and $y=de^{-2t}$ where $c$ and $d$ are constants.

Answer 2

This system is just a collection of 2 uncoupled ODEs, and so can be solved separately, just as we would a simple 1st order ODE.