Suppose that $\vect{x},\,\vect{y}\in\complex{n}$, $\vect{b}\in\complex{m}$ and $A$ is an $m\times n$ matrix. If $\vect{x}$, $\vect{y}$ and $\vect{x}+\vect{y}$ are each a solution to the linear system $\linearsystem{A}{\vect{b}}$, what can you say that is interesting about $\vect{b}$? Form an implication with the existence of the three solutions as the hypothesis and an interesting statement about $\linearsystem{A}{\vect{b}}$ as the conclusion, and then give a proof.