Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 3 - Linear Systems - 3-1 Solving Systems Using Tables and Graphs - Practice and Problem-Solving Exercises - Page 140: 45

Answer

sometimes true

Work Step by Step

The given statement is sometimes true because if $b=3$, then the $y$-intercepts of the lines would be the same, providing at least one solution. If the slopes of these lines were the same, the lines would be coinciding, causing an infinite amount of solutions. If the slopes are different, the lines would have exactly one solution. Since we do not know what the slopes are, we can conclude that if b=3, the statement would sometimes have one solution.
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