Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.4 Solve Systems of Linear Equations in Three Variables - 3.4 Exercises - Skill Practice - Page 183: 29

Answer

$(-4,5,-4)$ is the solution of the system.

Work Step by Step

Using elimination for the first two equations: $2x - y + 2z =-21 $ $x + 5y - z = 25$ Multiply both sides of the second equation by $-2$: $2x - y + 2z =-21 $ $-2x -10y +2z = -50$ ______________________________ $-11y+4z=-71$ (1) Then continue to use elimination for the second and the third equations: $-3x + 2y + 4z = 6 $ $x + 5y - z = 25$ Multiply both sides of the second equation by $3$: $-3x + 2y + 4z = 6 $ $3x + 15y - 3z = 75$ ________________________ $17y+z=81$ (2) Using elimination for equations (1) and (2): $-11y+4z=-71$ $17y+z=81$ Multiply both sides of the second equation by $-4$: $-11y+4z=-71$ $-68y-4z=-324$ _____________ $-79y=-395$ $y=5$ Solve for z: $17y+z=81$ $17(5)+z=81$ $z=-4$ Solve for x: $2x-y+2z=-21$ $2x-5+2(-4)=-21$ $2x=-8$ $x=-4$ $(-4,5,-4)$ is the solution of the system.
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