Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - Chapter 7 Test - Page 484: 19

Answer

See below:

Work Step by Step

Step I: In the given above expressions, replace inequalities with equality, and draw it: \[\begin{align} & 2x-y=4; \\ & \text{And, }2x-y=-1 \end{align}\] In the first equation, \[\begin{align} & x-\text{intercept}=2 \\ & y-\text{intercept}=-4 \\ \end{align}\] In the second equation, \[\begin{align} & x-\text{intercept}=-\frac{1}{2} \\ & y-\text{intercept}=1 \\ \end{align}\] Step II: Put\[x=0,\text{ and }y=0\], in the inequalities equations. In the first inequality: \[0\le 4\]; it is true. In the second inequality: \[0>-1\]; it is also true. Therefore, both the inequalities contain the origin. Graph does not include the line 2x – y = -1 but it includes 2x – y = 4
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