Finding subspaces for a nonhomogeneous system 
Show that the solution vectors of a consistent nonhomogeneous system of m linear equations in n unknowns do not form a subspace of $\mathbb{R}^n$.

I'm not really sure how to go about this problem. I know that I'm suppose to check if the vectors are with the subspace by addition and scalar multiplication but I'm not really sure how to set it up. 

If we have a consistent nonhomogeneous system $Ax = y$ with a solutions $x_0$ and $x_1$, then $A(x_0 - x_1) = Ax_0 - Ax_1 = y - y = 0$. But if we assume that the solutions to the nonhomogeneous system form a subspace, then $x_0 - x_1$ must also be a solution to the nonhomogeneous system, thus $0 = A(x_0 - x_1) = y$. This is clearly false, so the solutions to the nonhomogeneous system do not form a subspace.
Or, even easier, $0$ must be an element of any subspace (since $x - x = 0$) but $A0 = 0 \ne y$.
