Elimination theory

Elimination theory is a branch of algebra focused on solving systems of polynomial equations by reducing multiple equations to a single one, called the resultant. This process involves eliminating variables step-by-step, allowing us to find common solutions more efficiently. Think of it as removing variables to narrow down the possibilities, making it easier to determine where solutions exist. It is a fundamental concept in algebra that helps mathematicians understand when and how equations share solutions, especially when dealing with complex, multi-variable systems.