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 - 7.4 Linear Inequalities in Two Variables - Exercise Set 7.4 - Page 454: 28

Answer

See below:

Work Step by Step

Substitute the coordinates of origin in the given system of inequalities and check whether the inequalities are true or not as: \[\begin{align} & 2x-y<3 \\ & 2\left( 0 \right)-0<3 \\ & 0+0<3 \\ & 0<3 \end{align}\] The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[2x-y<3\]. And, \[\begin{align} & x+y<6 \\ & 0+0<5 \\ & 0<6 \end{align}\] The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[x+y<6\]. Thus, the graph of the system of linear inequalities, \[\begin{align} & 2x-y<3 \\ & x+y<6 \\ \end{align}\]is the common region of both the graphs and is shown below:
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