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

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. In this context, they indicate regions on a graph where one variable is greater than or less than another. Understanding how to interpret and graph inequalities is crucial for visualizing solution sets.

Graphing Linear Inequalities

Graphing linear inequalities involves plotting the boundary line of the inequality and determining which side of the line represents the solution set. A dashed line indicates that points on the line are not included in the solution, while a solid line means they are. The shading of the graph shows where the inequality holds true.

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. Analyzing systems of inequalities helps in finding common solutions and understanding the relationships between different constraints.