Explanation Given Information: The equations are: 2 y 2 + x y = 5 And 4 y + x = 7 Formula used: Use the zero-product rule to simplify the factors: ( a − b ) ( b − c ) = 0 Then a − b = 0 or b - c = 0 . Calculation: Consider the linear equations, 2 y 2 + x y = 5 …… (1) And 4 y + x = 7 …… (2) Solve the above equation in terms of x : 4 y + x = 7 x = − 4 y + 7 …… (3) Now substitute the value of x = − 4 y + 7 in equation, ( 1 ) , and solve it. 2 y 2 + x y = 5 2 y 2 + ( − 4 y + 7 ) y = 5 2 y 2 + ( − 4 y 2 + 7 y ) = 5 − 2 y 2 + 7 y − 5 = 0 Further, simplify, 2 y 2 − 7 y + 5 = 0 ( 2 y − 5 ) ( y − 1 ) = 0 Now simplify both the factors using zero-product rule, 2 y − 5 = 0 y = 5 2 And y − 1 = 0 y = 1 Now substitute y = 5 2 in the equation, ( 3 ) , and solve for x : x = − 4 y + 7 = − 4 ( 5 2 ) + 7 = − 10 + 7 = − 3 The ordered pair is ( − 3 , 5 2 ) . Now substitute y = 1 in the equation, ( 3 ) , and solve for x : x = − 4 y + 7 = − 4 ( 1 ) + 7 = 3 The ordered pair is ( 3 , 1 )

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Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 13.4, Problem 20ES

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To calculate: The solution of the equations 2y2+xy=5, 4y+x=7.

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Chapter 13.4, Problem 19ES

Chapter 13.4, Problem 21ES

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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. 1ES Ch. 13.1 - Prob. 2ES Ch. 13.1 - Choose from the following list the word that best...Ch. 13.1 - Choose from the following list the word that best...Ch. 13.1 - Prob. 5ES

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The solution of the equations 2 y 2 + x y = 5 , 4 y + x = 7.

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To calculate: The solution of the equations 2y2+xy=5, 4y+x=7.

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Chapter 13 Solutions