In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x+y>4, x+y>−1

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They can be represented using symbols such as '>', '<', '≥', and '≤'. In this context, the inequalities define regions on a graph where certain conditions hold true, which is essential for graphing the solution set.

Graphing Linear Inequalities

Graphing linear inequalities involves plotting the corresponding linear equation and then determining which side of the line represents the solution set. For example, the inequality '2x - y > 4' can be graphed as a dashed line, indicating that points on the line are not included in the solution, and the area above the line represents the solutions.

System of Inequalities

A system of inequalities consists of two or more inequalities that must be satisfied simultaneously. The solution set is the region where the shaded areas of all inequalities overlap on the graph. Understanding how to find this intersection is crucial for determining if a solution exists and for graphing the complete solution set.