# Can integer linear programs have non-integer OPT solutions?

Why is it that every integer linear program has optimal solutions that are integers? At least in online text books, they are always integers. Can solutions of ILPs only be integers?

\begin{cases} \begin{alignat}{1} 2 &\cdot x \le 1 \\[1.5ex] -2 &\cdot x \le -1 \end{alignat} \end{cases}