Lesson Summary A system of linear equations can have a unique solution, no solution, or infinitely many solutions. Systems with a unique solution are comprised of two linear equations whose graphs have different 510 pes coordinate plane will be two distinct lines that intersect at only one point. Systems with no solutions are comprised of two linear equations whose graphs have the same coordinate plane will be two parallel lines (with no intersection). Systerms with infinitely many solutions are comprised of two linear equations whose graphs have the same graphs in a coordinate plane are the same line (i.e., every solution to one equation will be a solution to the other equation).

Did you know that the study of linear equations dates back to ancient civilizations? The Babylonians, as early as 2000 BC, used geometric methods to solve problems that can be modeled with linear equations today! Fast forward to the Renaissance, and mathematicians like Descartes helped lay the groundwork for what we now know as coordinate geometry. In real life, systems of linear equations come in handy more than you might think! For instance, if you’re planning a road trip and need to determine when two cars will meet if they start from different points and travel at different speeds, you can use a system of linear equations. By plotting their routes, you can visualize when and where they intersect—just like in the examples of unique, no, or infinitely many solutions!