Solving a 2 x 2 System Using Matrix Row Operations (Gauss Jordan Row Reduced Echelon Form)

Learn how to solve a 2x2 system of linear equations using augmented matrices and row operations to transform the matrix into Row Reduced Echelon Form (RREF)! This powerful matrix method is an alternative to substitution, elimination, or graphing. In this math tutorial, I walk you through two complete examples, step-by-step, showing you the exact elementary row operations needed to find the point of intersection for both systems. You will learn the exact sequence of operations to ensure you don't undo your previous work, following a simple counter-clockwise approach. Key concepts covered in this video: How to write a 2 x 2 system as an augmented matrix using the coefficients. The three elementary row operations (exchanging rows, multiplying a row by a non-zero number, and adding rows). The goal: achieving an identity matrix on the left (ones on the diagonal, zeros everywhere else). Finding the solution $(x, y)$ from the final matrix form. If you are ready to apply this method to more complex problems, check out my next video on how to solve a 3x3 system using the same augmented matrix row operations! https://youtu.be/fIOYcBIhvS0 ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join