Graphical Approach to Simultaneous Equations and Inequalities

① This example demonstrates how to solve simultaneous equations and inequalities graphically by visualizing intersections and feasible regions in a dynamic geometry environment. ② Core mathematical concepts include solutions of linear equation systems, feasible regions of linear inequalities, perpendicular lines, intersections, and the combination of polygons with stochastic processes. ③ Construction details: using GeoGebra commands such as Intersect to find intersection points, OrthogonalLine to construct perpendiculars, Segment to draw segments, and Point to define key points; objects include lines r and s, points A, B, C, H, texts text1 and text2, functions f and g, and shapes F, G, h, i, K, j, e, D, I, which together illustrate solution sets via intersections and region partitioning. ④ Suitable for middle and high school mathematics teaching to understand the geometric meaning of simultaneous equations and inequalities, also useful for pre-university review or for teachers creating interactive lessons.