Explanation The given system is { x 2 + y 2 = 26 x 2 − 2 y 2 = 23 . Name the system as, { x 2 + y 2 = 26 ( 1 ) A circle x 2 − 2 y 2 = 23 ( 2 ) A hyperbola . Rewrite equation (1) as y 2 = 26 − x 2 . Substitute x 2 + y 2 = 26 in (2) and solve for x . x 2 − 2 ( 26 − x 2 ) = 23 x 2 − 52 + 2 x 2 = 23 3 x 2 = 75 x 2 = 25 x = ± 5 Substituting x = ± 5 in x 2 + y 2 = 26 . ( ± 5 ) 2 + y 2 = 26 25 + y 2 = 26 y 2 = 26 − 25 y = ± 1 Therefore, the solution set of the given system of equation is, { ( − 5 , − 1 ) , ( − 5 , 1 ) , ( 5 , − 1 ) , ( 5 , 1 ) } . Check the solution as follows. ( − 5 , ± 1 ) : ( − 5 ) 2 + ( ± 1 ) 2 = 26 ( Equation 1 ) 25 + 1 = 26 26 = 26 True ( − 5 , ± 1 ) : ( − 5 ) 2 − 2 ( ± 1 ) 2 = 23 ( Equation 2 )

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ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 12, Problem 60RE

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Chapter 12, Problem 59RE

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The given system of nonlinear equations using the method of substitution.

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