Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.2 - 3 x 3 Systems of Equations - Problem Set 11.2: 32

Answer

Infinitely many solutions

Work Step by Step

In order to find out if the equation has infinitely many solutions or no solution (the null set), we multiply each of the three equations by a constant so that when the equations are added, all of the variables cancel. If the resulting expression is true, the solution set is all real solutions, while if the resulting statement is false, there is no solution. Thus, we multiply the first equation by 2, the second equation by 1, and the bottom equation by -1. We then add them to obtain: $0 = 12 - 10 -2 \\ 0 = 0$ There are infinitely many solutions.
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