Explanation Given Information: The equations are: x 2 + y 2 = 9 And 25 x 2 + 16 y 2 = 400 Calculation: Consider the linear equations, x 2 + y 2 = 9 …… ( 1 ) And, 25 x 2 + 16 y 2 = 400 …… ( 2 ) Now multiply equation ( 1 ) by − 16 , − 16 x 2 − 16 y 2 = − 144 …… ( 3 ) Now add both the equations ( 2 ) and ( 3 ) , ( 25 x 2 − 16 x 2 ) + ( 16 y 2 − 16 y 2 ) = 400 − 144 9 x 2 = 256 x 2 = 256 9 x = ± 16 3 Now simplify both the factors, x = 16 3 And x = − 16 3 Now substitute x = 16 3 in the equation, ( 1 ) and solve for y : x 2 + y 2 = 9 ( 16 3 ) 2 + y 2 = 9 256 9 + y 2 = 9 y 2 = 9 − 256 9 Further simplify, y 2 = − 175 9 y = ± − 175 9 y = ± 5 7 3 i The ordered pair is ( 16 3 , 5 7 3 i ) and ( 16 3 , − 5 7 3 i ) . Now substitute x = − 16 3 in the equation, ( 1 ) and solve for y : x 2 + y 2 = 9 ( − 16 3 ) 2 + y 2 = 9 256 9 + y 2 = 9 y 2 = 9 − 256 9 Further simplify, y 2 = − 175 9 y = ± − 175 9 y = ± 5 7 3 i The ordered pair is ( − 16 3 , 5 7 3 i ) and ( − 16 3 , − 5 7 3 i ) . The following graph serves as a check and as roots are imaginary so graph will not intersect at any point. Imaginary roots are ( 16 3 , 5 7 3 i ) , ( 16 3 , − 5 7 3 i ) , ( − 16 3 , 5 7 3 i ) and ( − 16 3 , − 5 7 3 i ) . Check: For the ordered pair ( 16 3 , 5 7 3 i ) : Consider equation ( 1 ) , x 2 + y 2 = 9 ( 16 3 ) 2 + ( 5 7 3 i ) 2 = ? 9 256 9 − 175 9 = ? 9 9 = 9 Now, consider equation ( 2 )

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

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ISBN: 9780137361847

Author: Marvin Bittinger, David Ellenbogen

Publisher: PEARSON+

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Chapter 13.4, Problem 33ES

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To calculate: The solution of the equations x2+y2=9, 25x2+16y2=400

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Chapter 13.4, Problem 32ES

Chapter 13.4, Problem 34ES

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Chapter 13 Solutions

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

Ch. 13.1 - Prob. 1YT Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 5YT Ch. 13.1 - Prob. 1CYU Ch. 13.1 - Prob. 2CYU Ch. 13.1 - Prob. 3CYU Ch. 13.1 - Prob. 4CYU Ch. 13.1 - Prob. 5CYU

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The solution of the equations x 2 + y 2 = 9 , 25 x 2 + 16 y 2 = 400

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Chapter 13 Solutions