Understanding linear systems of equations
Equations of two variables whose graphs are straight lines, or linear equations, are one of the core parts of any elementary algebra course. They model simple proportional relationships well, but several linear equations taken at once, perhaps involving more than just two variables, allow for the modeling of much more complex situations, as we will see.
In this section, we discuss these familiar equations and then consider the idea of a system of multiple linear equations that we wish to solve all at once. We also define linear equations and systems of linear equations that involve more than just two variables and show how to solve them by hand.
Definition – Linear equations in two variables
A linear equation of the variables x1 and x2 is any equation that can be written in the form a1x1 + a2x2 = b for some real numbers a1, a2, and b. The solutions of the equation are all ordered pairs (x1, x2) 
R2 that satisfy the equation...
