Solving Systems of Quadratic Equations Algebraically and Graphically

The Organic Chemistry Tutor

This educational video provides a clear, step-by-step tutorial on solving systems of equations that include quadratic functions. The narrator demonstrates how to solve these systems algebraically using the substitution method and then verifies the results graphically. The video moves from a system containing one linear and one quadratic equation to a more complex system involving two quadratic equations. Key themes include algebraic manipulation, factoring quadratic expressions, and the geometric interpretation of algebraic solutions. The video covers essential skills such as setting expressions equal to each other, combining like terms, solving for variables by factoring, and calculating corresponding coordinates. It also highlights the use of technology, specifically online graphing calculators like Desmos, to visualize the points of intersection. For educators, this video serves as an excellent resource for bridging the gap between algebraic procedures and graphical understanding. It reinforces the concept that the solution to a system of equations represents the specific points where their graphs intersect. The clear pacing and dual-method approach make it valuable for helping students self-check their work and understand the "why" behind the algebraic steps.