Algebra Know-It-ALL

294 Larger Linear Systems

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!

1. Here are the three revised original equations for the three-by-three system we tackled in
   this chapter:

− 4 x+ 2 y− 3 z= 5

2 x− 5 y−z=− 1

3 x+ 6 y− 7 z= 0

In the section “Eliminate One Variable,” we got rid of z between the first two of these

equations, and then between the second two. Now eliminate z between the first and third

equations.

x

y

(–3,3)

(0,–3)

(4,5)

(2,5)

(0,–1)

(0,1)

y=x+ 1

y= –2x– 3

y= 3x– 1

Each axis

increment

is 1 unit

Figure 18-3 Graphs of three equations in two variables,

considered as a linear system. There is no

solution, because there is no single point

common to all three lines. On both axes,

each increment represents 1 unit.