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: 86

Answer

Because the system will always have at least one solution $x=0, \quad y=0, \quad z=0$.

Work Step by Step

On the right side of each equation will be zero. At $x=0$ and $y=0$ this will be true for all of the equations because on the left all of the terms will be zero as well. So there is always one solution $x=0$ and $y=0$ that satisfies all of the equations and thus they are consistent. Graphically the lines in $xy$ plane represented by these equations will all pass through the origin and so the origin will be a common point of intersection.
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