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: 14


Infinitely many solutions.

Work Step by Step

Eq. 1: $\frac{1}{2}x - \frac{1}{3}y$ = 1 Eq. 2: $-2x + \frac{4}{3}y$ = -4 If we multiply equation 1 by -4, the equation will become: -4($\frac{1}{2}x - \frac{1}{3}y$) = -4(1) $\frac{-4}{2}x - \frac{-4}{3}y$ = -4 $-2x + \frac{4}{3}y$ = -4 Equations 1 and 2 are the same. Their graphs will coincide, meaning that all points on one line overlay all points on the other, so every point will be a solution. Plugging values in for both equations will return the same answer for every point in both equations. Therefore, there are infinitely many solutions.
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