By definition, parallel lines have the same slope, in which they have no point of intersection. Therefore, they will have no solution (making them an inconsistent system).
Out of all the given options, the inequality statements in Option C has the same slope of 1 (regardless of the inequality symbol, what matters is their lack of point of intersection because their lines are parallel).
Therefore, the correct answer is Option C: y ≥ x + 1; y ≤ x - 1.
