281CHAPTER18 Larger Linear Systems
In this chapter we’ll solve a three-by-three linear system. That’s a triplet of linear equations in
three variables. There are numerous ways to tackle problems of this sort. We’ll look at only
one example and one method. The scheme presented here can be broken down into three
major steps:- Eliminate one variable to get a two-by-two system
- Solve that two-by-two system for both of its variables
- Solve for the original eliminated variable by substitution
Eliminate One Variable
Consider three linear equations, each having three variables: x, y, and z. Our mission: Find
the numbers for x, y, and z that satisfy all three equations. Here is the system we’ll solve in
this chapter:− 4 x+ 2 y− 3 z= 5
2 x− 5 y=z− 1
3 x=− 6 y+ 7 zChoose the vanishing variable
Let’s decide which variable we want to eliminate. It doesn’t make any difference whether it’s
x, y, or z. If we do all the calculations right, we’ll get the same answer in the end, no matter
which variable we choose at this stage. Let’s get rid of z, so we are left with two equations in
x and y.Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.