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: 92

Answer

The solution is $x=300$ and $y=315$. This mean that the two graphs intersect. Their slopes are so similar that on the scale presented on the graph they seem almost parallel. To see that they are not parallel, the range of $x$ should be increased.

Work Step by Step

We will first solve this system: Step 1: Express $y$ in terms of $x$ from the first equation: $$20y=21x\Rightarrow y=\frac{21}{20}x$$ Step 2: Put this into the second equation and find $x$: $$13x-12\times\frac{21}{20}x=120$$ which becomes $$13x-\frac{63}{5}x = 120\Rightarrow \frac{2}{5}x=120$$ and this gives $$x=120\times\frac{5}{2} = 300.$$ Step 3: Use this calculated value for $x$ to find $y$: $$y=\frac{21}{20}\times 300 = 315.$$ The solution is $x=300$ and $y=315$. This mean that the two graphs intersect. Their slopes are so similar that on the scale presented on the graph they seem almost parallel. To see that they are not parallel, the range of $x$ should be increased.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.