Systems of Linear Inequalities

A system of linear inequalities is a set of multiple conditions involving quantities (variables) that must be satisfied simultaneously. Each inequality defines a region in a coordinate plane, representing all possible solutions that make the inequality true. When combined, these conditions carve out a common area—called the feasible region—where all inequalities overlap. This concept is used to model real-world problems like budgeting or resource allocation, where constraints must be met collectively. Solutions within this region satisfy all the individual inequalities, helping identify acceptable options or optimal solutions within given limits.