Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Section 4.2 - Solving Systems of Linear Equations in Three Variables - Vocabulary, Readiness & Video Check - Page 219: 2

Answer

equations a, c, d

Work Step by Step

Substituting the given point $ (2,1,-4) ,$ in the choices results to \begin{array}{l}\require{cancel} \text{a. }\\ x+y+z=-1 \\\\ 2+1+-4=-1 \\\\ -1=-1 \text{ (TRUE)} \\\\ \text{b. }\\ x-y-z=-3 \\\\ 2-1-(-4)=-3 \\\\ 2-1+4=-3 \\\\ 5=-3 \text{ (FALSE)} \\\\ \text{c. }\\ 2x-y+z=-1 \\\\ 2(2)-1+(-4)=-1 \\\\ 4-1-4=-1 \\\\ -1=-1 \text{ (TRUE)} \\\\ \text{d. }\\ -x-3y-z=-1 \\\\ -2-3(1)-(-4)=-1 \\\\ -2-3+4=-1 \\\\ -1=-1 \text{ (TRUE)} .\end{array} Hence, $\text{ equations a, c, d }$ has the given point as solution.
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