# Differential equations systems

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!

• Actually the method you are using is more complicated than what you need here! Can you think of any function whose derivative would be minus itself? ($f' = -f$) – Milloupe Jun 17 at 9:35

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.