A system of linear equations consists of multiple linear equations. The solution to a linear system, if one exists, is usually the point that all of the equations have in common. Occasionally, the solution will be a set of points.
There are four commonly used tools for solving linear systems: graphing, substitution, linear combination, and matrices. Each has its own advantages and disadvantages in various situations, however I often wondered about why the linear combination approach works. My earlier post explains why it works from an algebraic perspective. This post will try to explain why it works from a graphical perspective.
Consider the linear system:
which, when graphed, looks like: Continue reading Linear Systems: Why Does Linear Combination Work (Graphically)?