Algebra Know-It-ALL

264

CHAPTER

17 Two-by-Two Linear Graphs

Let’s graph the two-by-two linear systems we looked at in Chap. 16. This will give you a

chance to see what’s going on when a system has a single solution (is consistent), has no solution

(isinconsistent), or has infinitely many solutions (is redundant or dependent). Any linear system

must fall into one of these three categories.

We Morphed, We Mixed, We Can Graph

In the preceding chapter, we used the morph-and-mix method to solve the following linear

system for x and y:

8 x+ 4 y= 16

and

7 x−y= 41

We found that x= 5 and y=−6. Now we’ll illustrate this situation graphically, calling x the

independent variable and y the dependent variable.

Find two points for each line

When we want to physically draw a graph of a line on graph paper, we must know the

coordinates of two points that lie on that line. We can then connect the two points, imag-

ining the line extending forever in either direction. When we want to graph a two-by-two

linear system, the most efficient approach is to find the points where the two lines cross

one of the axes, and then also find the point where the two lines intersect (if there is such

a point).

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