Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - Review Exercises - Page 35: 19


$x_{1}=-\frac{1}{2}$ $x_{2}=\frac{4}{5}$ $(-\frac{1}{2},\frac{4}{5})$

Work Step by Step

$0.2x_{1}+0.3x_{2}=0.14$ $0.4x_{1}+0.5x_{2}=0.20$ Multiply the first equation by $-2$. $-0.4x_{1}-0.6x_{2}=-0.28$ $0.4x_{1}+0.5x_{2}=0.2$ Eliminate the $x_{1}$-variable by addition of the two equations. $-0.1x_{2}=-0.08$ $x_{2}=0.8=\frac{4}{5}$ Substitute for $x_{2}$ and solve for $x_{1}$. $0.2x_{1}+0.3\times0.8=0.14$ $0.2x_{1}=-0.1$ $x_{1}=-0.5=-\frac{1}{2}$
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