Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.2 - Systems of Linear Equations in Several Variables - 10.2 Exercises - Page 697: 19

Answer

$x=1$ $y=-1$ $z=5$

Work Step by Step

Express y from the second equation. $x+2y-z=-6$ $y-3z=-16\rightarrow y=-16+3z$ $x-3y+2z=14$ Substitute $ y=-16+3z$ into the first and the third equation. $x+2(-16+3z)-z=-6$ $x-3(-16+3z)+2z=14$ Simplify. $x+5z=26$ $x-7z=-34$ Multiply the second equation by -1. $x-7z=-34 \rightarrow -x+7y=34$ Add the equations to eliminate x. $12z=60$ $z=5$ Substitute for z and solve for x and y. $x+5z=26 \rightarrow x=1$ $y=-16+3z \rightarrow y=-1$
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