I have a linear program
$\max 3x_1+x_2\quad$ s.t. $\quad\begin{matrix} x_1-x_2&\leq& -1\\ -x_1-x_2&\leq& -3 &(*)\\ 2x_1+x_2&\leq& 2&(**)\\ x_1,x_2&\geq& 0 \end{matrix}$
I solved this and got $x_1=1, x_2=2$ for the optimal solution, but after a second look at the restrictions, I noticed that when adding $(*)$ and $(**)$ I get $x_1\leq -1$. Isn't this a contradiction to $x_1\geq 0$?