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: 91

Answer

The solution is$$x=39600,\quad y=398$$ So we see that there is a solution $x=39600$ and $y=398$ and this means that the graphs should intersect. And they do intersect because they are not exactly parallel. Their slopes are just so similar that you cannot notice that they are not parallel on this particular segment of $x$ that ranges from $-3$ to $4$. You would need a range measured in tens of thousands.

Work Step by Step

We will firs solve the system Step 1: Subtract the second equation from the first one to eliminate $x$: $$100y-99y-x-(-x) = 200-(-198)$$ which becomes $$y=398$$ Step 2: Put this into the first equation to find $x$: $$100\times 398 -x = 200\Rightarrow 39800-x=200$$ and this gives $$x=39800-200=39600$$ So we see that there is a solution $x=39600$ and $y=398$ and this means that the graphs should intersect. And they do intersect because they are not exactly parallel. Their slopes are just so similar that you cannot notice that they are not parallel on this particular segment of $x$ that ranges from $-3$ to $4$. You would need a range measured in tens of thousands.
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