Gaussian elimination applied to systems of linear equations

Gaussian elimination is a method used to solve systems of linear equations by transforming the equations into a simpler form. It works by performing specific operations—like swapping equations, multiplying them by constants, or adding/subtracting them—to eliminate variables step-by-step. This process creates a easier-to-solve triangular system, where variables can be found starting from the last equation and working backwards. Essentially, it's a systematic way to uncover the values of the unknowns by simplifying the relationships between equations, making the solution process more straightforward and organized.