Graphing a System of Three Linear Inequalities

This example demonstrates how to graph three linear inequalities on the same coordinate plane, using labeled points in each region so students can substitute the point values to determine which parts of the plane satisfy the entire system. The key math concepts include linear inequalities, solution sets represented as regions, boundary-line behavior (closed vs. open boundaries), and checking feasibility by substitution. In construction, the GeoGebra setup relies on many point objects—such as a, b, c, A–G, D/E points—and systematically labeled test points (A1–A7, B1–B7, C1–C7, D1–D7, E1–E2) to place sample coordinates inside different regions for verification. This makes it well-suited for interactive learning: students evaluate the inequalities at the labeled points and infer the solution area. Suitable for middle and high school learners studying inequalities and graphing, as well as for classroom demonstrations and guided practice.