Solving Linear Systems Graphically: Visual Verification of Intersections

① This applet demonstrates how the solution to a system of two linear equations corresponds to the intersection point of their graphs, allowing students to visually confirm algebraic results. ② Core mathematical concepts include linear equations, linear functions, systems of equations (unique, no, or infinite solutions), slope, intercept, and the geometric meaning of intersection. ③ Construction details: The applet uses GeoGebra commands such as Intersect to find the crossing point of two lines, FractionText to display solutions as fractions, Textfield and InputBox for interactive equation entry, button1 to trigger verification, Point objects (A, B, C, D) to mark key locations, and text1–text6 for instructions and feedback, creating a workflow of 'solve by hand → input → verify graphically'. ④ Suitable for middle school to high school students learning systems of linear equations, and useful for teachers in classroom demonstrations or for students as a self-check tool to reinforce the concept that the solution is the intersection point.