This is the 2nd video in the "What to eat for breakfast?" series. In this video, we demonstrate 1) how to verify a given ordered 2-tuple is a solution to a given linear equation; 2) how to visualize the set of solutions to a given linear equation about two unknowns in the x-O-y plane; 3) present the fact that a linear equation about two unknowns has infinitely many solutions. In fact, the set of its solutions contains all the ordered 2-tuples that correspond to points on a certain straight line. (video link needs to be updated. then add more tags)
We will motivate our study of linear algebra by considering the problem of solving several linear equations simultaneously. The word solve tends to get abused somewhat, as in “solve this problem.” When talking about equations we understand a more precise meaning: find all of the values of some variable quantities that make an equation, or several equations, simultaneously true.