Graphical Solution of Simultaneous Linear and Quadratic Equations

This GeoGebra example demonstrates the graphical solution of a system consisting of a linear equation and a quadratic equation by plotting a straight line and a parabola on the same coordinate plane and identifying their intersection points. Core mathematical concepts include quadratic functions, linear functions, simultaneous equations, coordinate geometry, and the correspondence between algebraic solutions and graph intersections. The construction relies on the GeoGebra Intersect command applied to objects m, b, a₁, a, B, c, d, A, and C, enabling dynamic visualization of how the line and curve meet. It is suitable for middle and high school mathematics instruction, particularly algebra and analytic geometry courses, and can be used for classroom demonstrations, student exploration, or homework practice to reinforce the concept that solutions to simultaneous equations correspond to intersection points of their graphs.