Simultaneous Equations: 5 Lines, 10 Intersections

①This example visualizes a system of five linear equations by drawing five lines and marking all ten pairwise intersections, demonstrating that each intersection corresponds to a solution of a pair of equations. ②Core mathematical concepts include systems of linear equations, intersection points, simultaneous solving, and the geometric-algebraic connection. ③Construction highlights: using GeoGebra's Intersect command on objects such as lines a, b, c, d, e and points H, I, K, L, O, P, Q, R, S, T to compute and display all intersection points, making the complete pairwise crossing structure visible. ④Suitable for middle-to-high school mathematics, especially for teaching linear systems, coordinate geometry, or as an interactive demonstration in algebra classes.