A system of linear equations consists of multiple linear equations. You can think of this as multiple lines graphed on one coordinate plane.Â Three situations can arise when looking at such a graph. Either:

1) No point(s) are shared by all lines shown

2) There is one point that all lines cross through

3) The lines lie on top of one another, so there are many points that the lines have in common.

There are four commonly used tools for solving linear systems:

– graphing

– substitution

– linear combination

– matrices

Each has its own advantages and disadvantages in various situations, however I often used to wonder 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)?