Sum of all simple submodules

Question

Let $M$ be an $A$-module where $A$ is a $k$-algebra ($k$ an algebraically closed field). If $\operatorname{Soc}{(M)}$ denotes the socle of $M$, i.e the sum of all simple submodules of $M$ why is that that if $N$ is a nonzero submodule of $M$ then $N$ has non trivial intersection with $\operatorname{Soc}{(M)}$?

Answer 1

Prove that the socle of every non-zero finite dimensional module is non-zero. In other words, that every non-zero finite dimensional module contains a simple one.

Can you see how to use this to conclude?