We have that system of differential equations:

$$\{\begin{array}{l}{x}^{\prime}=-x\\ {y}^{\prime}=-2y\end{array}$$

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.