Here's something I found interesting. "If and , find the abscissa of a point which is on the graphs of both and ."
I really didn't know how to do it; the book certainly didn't spell it out anywhere. I started by graphing both equations, getting a rough idea of where the equations crossed, and plugged in a couple of points until I found the point . Then I just happened to notice that earlier I had tried simplifying , which simplifies to , and that those numbers corresponded to the abscissa of the point in question. (Never mind that they also correspond to the numbers of the function ).
I tried a few other simple linear equations and got the same results, so I feel like I've stumbled upon a consistent solution to the problem. Obviously I haven't discovered anything new, but I wonder, is this solution valid to all sets of two linear equations? If so, is there a named theorem for it?