Verifying Solutions to Systems of Linear Equations

The Organic Chemistry Tutor

This video tutorial demonstrates how to determine if a specific ordered pair is a valid solution to a system of linear equations. The instructor walks through two distinct examples: one where the coordinate pair satisfies both equations (a valid solution) and one where it satisfies only the first equation but fails the second (not a solution). The method shown relies on direct substitution of x and y values. The content focuses on the fundamental concept that a solution to a system must satisfy every equation within that system simultaneously. It reinforces the skills of algebraic substitution, order of operations, and verifying mathematical claims. The video explicitly addresses the common student pitfall of stopping after checking only one equation. For educators, this resource serves as an excellent direct instruction piece or review tool for Algebra 1 students. It clarifies the definition of a "solution" in the context of systems before students learn to solve them via graphing, substitution, or elimination. The clear, step-by-step visual working makes it accessible for students who struggle with abstract definitions.