A system of inequalities consists of two or more inequalities that share the same variables. These inequalities can represent various constraints or conditions in real-world situations, such as budget limits or resource availability. The solution to a system of inequalities is the set of all points that satisfy all the inequalities simultaneously, often represented graphically as a shaded region on a coordinate plane. To solve a system of inequalities, one can graph each inequality on the same coordinate plane. The overlapping region where all shaded areas intersect represents the solution set. This method is useful in fields like economics, engineering, and social sciences to analyze feasible solutions under given constraints.