Solving Systems of Equations with Three Variables and Real-World Applications

The Organic Chemistry Tutor

This instructional math video provides a detailed walkthrough on solving systems of linear equations using the elimination method. The video begins by tackling a complex system involving three variables (x, y, and z) and three equations. The narrator demonstrates a step-by-step process of eliminating variables to reduce the system to manageable two-variable equations, eventually solving for all three unknowns. The focus is on procedural fluency and the logic behind choosing which equations to combine to efficiently eliminate variables. The second half of the video shifts focus to applying these algebraic concepts to real-world word problems. Two distinct scenarios are explored: an investment problem involving interest rates and principal amounts, and a purchasing problem involving the unit costs of apples and bananas. In both cases, the narrator explicitly models how to translate text into algebraic equations, set up the system, and solve for the variables to answer the specific question asked. For educators, this video serves as an excellent resource for Algebra II or advanced Algebra I classrooms. It bridges the gap between abstract calculation and practical application, showing students not just "how" to calculate, but "why" these skills are useful for solving financial and logic problems. The clear, handwritten visual style helps focus attention on the mathematical steps without distraction, making it ideal for reviewing specific techniques or introducing the concept of multi-variable systems.