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 - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 42



Work Step by Step

$\frac{2}{3}x_1+\frac{1}{6}x_2=0$ $4x_1+x_2=0$ Express $x_2$ in terms of $x_1$ $x_2= -4x_1$ Substitute for $x_2$ in the first equation. $\frac{2}{3}x_1+\frac{1}{6}(-4x_1)=0$ $\frac{2}{3}x_1-\frac{4}{6}x_1=0$ $\rightarrow$ Multiply by 6 to remove fractions. $4x_1-4x_1=0$ $\rightarrow$ This expression is always true and therefore any pair of values which satisfy 1st or 2nd equation is a possible solution.
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