In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x+2y≤4, y≥x−3

Key Concepts

Graphing Inequalities

Graphing inequalities involves representing the solutions of an inequality on a coordinate plane. Each inequality can be graphed as a line, with a solid line indicating 'less than or equal to' or 'greater than or equal to,' and a dashed line for 'less than' or 'greater than.' The area that satisfies the inequality is shaded, showing all possible solutions.

System of Inequalities

A system of inequalities consists of two or more inequalities that are considered simultaneously. The solution set is the region where the shaded areas of all inequalities overlap. Understanding how to find this intersection is crucial for determining the feasible solutions that satisfy all conditions of the system.

Feasible Region

The feasible region is the area on a graph where all the inequalities in a system are satisfied. It is bounded by the lines of the inequalities and can be unbounded in some cases. Identifying this region is essential for solving optimization problems, where one seeks to maximize or minimize a particular objective function within the constraints defined by the inequalities.