Algebra Know-It-ALL

278 Two-by-Two Linear Graphs

(subtract 2 from s). Some of the resulting points are plotted in Fig. 17-8, along with the line connecting

them. The line is the graph of the function

s= 2 r− 3

Any point on the line (not only the ones plotted in the figure) can be called a solution to this redundant

two-by-two linear system. Because the domain and the range are both the entire set of real numbers, the

solution set (the set containing all the ordered pairs that satisfy the system) is not only infinite, but non-

denumerable!

Practice Exercises

This is an open-book quiz. You may (and should) refer to the text as you solve these problems.

Don’t hurry! You’ll find worked-out answers in App. B. The solutions in the appendix may not

represent the only way a problem can be figured out. If you think you can solve a particular

problem in a quicker or better way than you see there, by all means try it!

r

s

(0,–3)

(1,–1)

(2,1)

(3,3)

(4,5)

(–1,–5)

s= 2r– 3

Solutions =

all points

on line

• 10 r+ 5s+ 15 = 0

Each axis

increment

is 1 unit

Figure 17-8 Graphs of s= 2 r− 3 and − 10 r+ 5 s+ 15 = 0

as a two-by-two linear system where the

independent variable is r and the dependent

variable is s. The lines coincide because the

two equations are equivalent. On both axes,

each increment represents 1 unit.