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: 23


Answer A

Work Step by Step

The second equation: $3x - y + 4z = 8 $ $\rightarrow y=3x+4z-8$ Substitute for x in the first equation: $2x + 5y + 3z = 10$ $2x + 5(3x+4z-8) + 3z = 10$ $2x+15x+20z-40+3z=10$ $17x+23z=50$ (1) Substitute for x in the third equation: $5x - 2y + 7z = 12$ $5x-2(3x+4z-8)+7z=12$ $5x-6x-8z+16+7z=12$ $-x-z=-4$ $\rightarrow x=-z+4$ Substitute for x in equation (1): $17(-z+4)+23z=50$ $-17z+68+23z=50$ $6z=-18$ $z=-3$ Solve for x: $x=-(-3)+4=7$ Solve for y: $y=3.7+4(-3)-8=1$ $(7,1,-3)$ is the solution of the system. The correct answer is A.
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