I have been given the problem of solving the dual of the linear program
$$x_1-2x_2-x_3 \le -3 \\ 2x_1+3x_2-x_3 \ge -3\\x_1 \ge 0, x_2\ge 0, x_3\ge 0$$
I went ahead and reformulated the problem to the dual one and ended up with
$$-y_1+2y_2 \le -2\\ 2y_1+3y_2 \le -6\\ y_1 - y_2 \le -1\\ y_1\ge 0, y_2 \ge 0$$
The constraints of the dual problem however, leave me with an empty set. This confuses me, since the problem was formulated in a way that you expect the dual to have a solution. That's why I wanted to ask, whether or not I did make any mistakes in formulating the dual problem. Any help would be greatly appreciated!