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 - Problem Solving - Page 185: 47b


Each bouquet should include 8 roses, 2 lilies and 2 irises.

Work Step by Step

We have: $r+l+i=12$ $2.5r+4l+2i=32$ $r=2(l+i) \rightarrow r-2l-2i=0$ Use elimination for the first and third equations: $r+l+i=12$ $r-2l-2i=0$ Multiply both sides of the first equation by 2: $2r+2l+2i=24$ $r-2l-2i=0$ _____________________ $3r=24$ $r=8$ Substitute for r in the first equation: $8+l+i=12$ $l=4-i$ Substitute for r in the second equation: $2.5(8)+4(4-i)+2i=32$ $20+16-4i+2i=32$ $-2i=-4$ $i=2$ Solve for l: $l=4-i=4-2=2$
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