In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+6y≤6, 2x+y≤8

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as ≤ (less than or equal to) and ≥ (greater than or equal to) to indicate the range of possible solutions. Understanding how to manipulate and graph inequalities is crucial for solving systems of inequalities.

Graphing Systems of Inequalities

Graphing systems of inequalities involves plotting each inequality on a coordinate plane to visualize the solution set. The area where the shaded regions of the inequalities overlap represents the solutions that satisfy all inequalities in the system. This graphical representation helps in identifying feasible solutions and understanding the relationships between the inequalities.

Feasible Region

The feasible region is the area on a graph where all the constraints of a system of inequalities are satisfied. It is typically bounded by the lines representing the inequalities and can be unbounded in some cases. Identifying the feasible region is essential for determining the solutions to the system and for optimization problems in algebra.