College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.4 - Page 559: 15

Answer

(-1, 2) or (4, -3)

Work Step by Step

x + y = 1 can be written as y = 1 - x. Plug this into $x^{2} + xy - y^{2} = -5$ $x^{2} + x(1 - x) - (1 - x)^{2} = -5$ $x^{2} + x - x^{2} - 1 + 2x - x^{2} = -5$ $-x^{2} + 3x + 4 = 0$ Factor (x + 1)(-x + 4) = 0 x + 1 = 0 or -x + 4 = 0 x = -1 or 4 Plug the x-values into y = 1 - x y = 1 + 1 = 2 y = 1 - 4 = -3 (-1, 2) or (4, -3)
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