ABSTRACT
Many high school algebra courses devote time to systems of linear equations. Let us look at the following example:
− + =x x1 24 8 ,
3 6 301 2x x+ = .
Here, x1 and x2 are unknown quantities. Some algebra books denote x1 and x2 as x and y (or with other symbols); we use subscripts instead in anticipation of casting the quantities as elements of a vector. Now, each equation is the equation for a line. In other words, the set of points with coordinates ( , )x x1 2 on a two-dimensional Cartesian graph that satisfy the first equation is a line. Similarly, the set of points with coordinates x x1 2, on a two-dimensional Cartesian graph that satisfy the second equation is also a line, different from the first. We can rearrange the two equations a little to see better that the equations are in the more familiar form x intercept slope x2 1= + ×( ) ( ) :
x x2 12 1 4
= + ,
x x2 15 1 2
= − .
