Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 13 - Section 13.3 - Solving Nonlinear Systems of Equations - Practice: 4

Answer

$(\sqrt 6,\sqrt 5),(\sqrt 6,-\sqrt 5),(-\sqrt 6,\sqrt 5),(-\sqrt 6,-\sqrt 5)$

Work Step by Step

We use the elimination method to solve this system. To eliminate $X^2$ when we add the two equations, we multiply both sides of the second equation by -1. Then $(-1)(x^2-y^2)=(-1)(1)$ $-x^2+y^2=-1$ Add the above equation to the first equation, $4y^2=20$ $y^2=5$ $y=+/-\sqrt 5$ Let $y=\sqrt 5$ and $y=-\sqrt 5$ in either original equation. We choose the second equation. Let $y=\sqrt 5$, $x^2-(\sqrt 5)^2=1$ $x=+/-\sqrt 6$ Let $y=-\sqrt 5$, $x^2-(-\sqrt 5)^2=1$ $x=+/-\sqrt 6$ The solution set is $(\sqrt 6,\sqrt 5),(\sqrt 6,-\sqrt 5),(-\sqrt 6,\sqrt 5),(-\sqrt 6,-\sqrt 5)$
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