Show that any continuous-time signal $x(t)$ can be represented as $x(t)= x_e(t) + x_o(t)$
Substitute the last two equations into the first and it should be clear.

iI.e., if you have $x_e(t), x_o(t)$  given to you. Substitute these into the equation for $x(t)$ and you should see that both sides are equal to each other.  

(Note that this proves the equality, but doesn't prove that $x_e(t)$ is even or that $x_o(t)$ is odd.)