Graphing Systems of Inequalities to Find Solution Areas

Miacademy & MiaPrep Learning Channel

This instructional mathematics video guides students through the process of graphing systems of linear inequalities to find solution sets. Narrated by Justin, the video builds upon prior knowledge of graphing systems of equations, distinguishing that inequality systems result in an intersecting solution "area" rather than a single point. It demonstrates the step-by-step process of graphing lines in various forms (standard, slope-intercept, and point-slope), determining line solidity (dashed vs. solid), and identifying the correct shading regions using test points. The video covers two distinct examples of increasing complexity. The first example involves a system of two inequalities requiring students to convert from standard form and identify intercepts. The second, more advanced example introduces a system of three inequalities, resulting in a complex graph with multiple shaded regions. The video explicitly models the strategy of testing specific coordinate points within different graphical regions to verify where the solutions for all inequalities overlap. For educators, this resource serves as an excellent visual guide for Algebra I units on systems of inequalities. It visually reinforces the concepts of boundary lines and overlapping solution sets, which are often abstract for students. The video is particularly useful for demonstrating how to handle multiple formats of linear equations simultaneously and offers a reliable method (test points) for verifying answers in complex graphical situations.