Investigating Systems of Inequalities: Visualizing Feasible Regions

This GeoGebra example demonstrates how to explore systems of inequalities by visualizing their solution regions on a coordinate plane. It combines multiple linear and nonlinear constraints, such as linear equations, exponential functions, and possibly Pythagorean-related conditions, to show the intersection area that satisfies all inequalities. The core mathematical concepts include systems of inequalities, linear equations, exponential functions, and the geometric interpretation of feasible regions. The construction uses commands like Random and RandomPolynomial to generate random coefficients, Element to extract list items, Line to draw boundary lines, and If for conditional logic to distinguish feasible from infeasible areas. Objects include points (A, B, C, etc.), segments (a, b, c, etc.), lists (list1, list2, list3), text elements (text2 to text13), and a button (button1), suggesting interactive controls to refresh random conditions or toggle displays. This resource is suitable for high school students learning about inequalities, introductory linear programming, or the connection between algebra and geometry, as well as for pre-university mathematics demonstrations.