In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.
This
is a piecewise function. Refer to the textbook.

Key Concepts

Systems of Inequalities

A system of inequalities consists of two or more inequalities that share the same variables. The solution set is the region where the graphs of these inequalities overlap. Understanding how to graph each inequality and identify the feasible region is crucial for solving these systems.

Graphing Techniques

Graphing techniques involve plotting inequalities on a coordinate plane to visualize their solutions. This includes determining boundary lines, using dashed or solid lines to indicate whether points on the line are included, and shading the appropriate regions to represent the solutions. Mastery of these techniques is essential for accurately representing the solution set.

Piecewise Functions

A piecewise function is defined by different expressions based on the input value. Understanding how to interpret and graph piecewise functions is important, as they can affect the boundaries of the solution set in a system of inequalities. Recognizing the conditions under which each piece applies is key to solving related problems.