Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 12: 85

Answer

a) Common intersection of three lines. b) All three lines will match. c) No common intersection of three lines.
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Work Step by Step

All of these equations determine a line in $xy$ plane. a) If there is exactly one solution that means that all of the three lines intersect at one unique point. The value of $x$ and $y$ at that point are the solution to the system (Graph on the left). b) This means that all of the three lines are the same and all points on that one line are the solutions to the system (Graph in the middle). c) This means that the three lines have no common intersection point. They may be parallel to each other or each two may intersect in the different points . This means than no $x$ and $y$ can simultaneously satisfy all three equations and thus the system has no solution (Graph on the right).
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