Final answer:
A system of inequalities has no solution when there is no overlap between the regions they represent on a coordinate plane, meaning the inequalities do not intersect at any point.
Step-by-step explanation:
The question of which system of inequalities has no solution pertains to the study of graphing regions defined by several inequalities and finding their intersection, if it exists. A system of inequalities will have no solution if the inequalities represent regions with no points in common, meaning that they do not intersect at any point in the coordinate plane. For example, the system:
- y < x + 1
- y > -x - 2
- y < -2x + 3
might have no solution if the lines formed by each inequality create distinct regions that do not overlap. To determine if a system of inequalities has no solution, one would graph each inequality on the same coordinate plane and see if there is a region that satisfies all of them simultaneously. If no such region exists, the system has no solution.