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 - 7.3 Systems of Linear Equations in Two Variables - Exercise Set 7.3 - Page 446: 78

Answer

Does not make sense

Work Step by Step

When one of the equations has a variable on one side by itself, it’s easy to make substitution of it in other equation. Therefore, substitution method is easier than addition method. For example: Consider a system of equation, \[\begin{align} & x+y=6 \\ & y=2x \end{align}\] Here, in second equation variable y is in terms of variable x. So, it is easier to use substitution method rather than addition method. So, substitute \[y=2x\]in the first equation and solve x: \[\begin{align} & x+y=6 \\ & x+2x=6 \\ & 3x=6 \\ & x=2 \end{align}\] Now put the value of x obtained above, in \[y=2x\]: \[\begin{align} & y=2x \\ & y=2\cdot 2 \\ & y=4 \end{align}\] Hence, \[\left( 2,4 \right)\]is a solution of this system of equation. To solve this system of equation, one can use addition method also, but the substitution method is easier. When one of the equations has a variable on one side by itself, substitution method is easier than addition method. Hence, the provided statement does not make sense.
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