Systems of Equations on a Graph

① This interactive example lets students explore systems of linear equations by visualizing two straight lines on a coordinate plane and observing their intersection point. ② Core math concepts include linear equations, slope and intercept, solutions of systems (unique, none, or infinite), and the connection between line intersections and coordinate geometry. ③ Construction details: The GeoGebra commands Intersect and Polygon are used; objects include m_1, b_1, c, m_2, b_2, d representing slopes and intercepts of two lines, point A as the intersection, and auxiliary polygons; multiple text labels (text1 to text6) display equations and results. ④ Suitable for middle school to high school students learning the integration of algebra and geometry, ideal for classroom demonstration or self-exploration—by dragging sliders to change slopes and intercepts, students can see in real time how the solution of the system changes.