Explanation The system of equations is { 5 y 2 − x 2 = 1 x y = 2 . Use substitution method and obtain the value of x and y as follows. Solve the equation x y = 2 for y. x y = 2 x y y = 2 y x = 2 y Substitute x = 2 y in the equation 5 y 2 − x 2 = 1 . 5 y 2 − ( 2 y ) 2 = 1 5 y 2 − 4 y 2 = 1 5 y 2 ⋅ y 2 − 4 y 2 ⋅ y 2 = 1 ⋅ y 2 [ Multiply both the sides with y 2 ] 5 y 4 − y 2 − 4 = 0 Let u = y 2 in 5 y 4 − y 2 − 4 = 0 and simplify as follows. 5 u 2 − u − 4 = 0 5 u 2 − 5 u + 4 u − 4 = 0 5 u ( u − 1 ) + 4 ( u − 1 ) = 0 ( 5 u + 4 ) ( u − 1 ) = 0 On further simplification, 5 u + 4 = 0 or u − 1 = 0 5 u = − 4 or u = 1 u = − 4 5 or u = 1 Substitute u = − 4 5 in u = y 2 , y 2 = − 4 5 y = ± − 4 5 = ± 2 i 5 [ ∵ i = − 1 ] Substitute u = 1 in u = y 2 . y 2 = 1 y = ± 1 = ± 1 Substitute the values of y in x = 2 y . For y = 2 i 5 , x = 2 ( 2 i 5 ) = 5 i = − i 5 [ ∵ − i = 1 i ] For y = − 2 i 5 , x = 2 ( − 2 i 5 ) = − 5 i = − ( − i 5 ) [ ∵ − i = 1 i ] = i 5 For y = − 1 , x = 2 − 1 = − 2 For y = 1 , x = 2 1 = 2 Thus, the pairs are ( − i 5 , 2 i 5 ) , ( i 5 , − 2 i 5 ) , ( − 2 , − 1 ) and ( 2 , 1 ) . Substitute ( − i 5 , 2 i 5 ) in 5 y 2 − x 2 = 1 to check whether ( − i 5 , 2 i 5 ) is a solution or not. 5 ( 2 i 5 ) 2 − ( − i 5 ) 2 = ? 1 5 ( 4 i 2 5 ) − 5 i 2 = ? 1 − 4 + 5 = ? 1 [ ∵ i 2 = − 1 ] 1 = 1 True Substitute ( − i 5 , 2 i 5 ) in x y = 2 to check whether ( − i 5 , 2 i 5 ) is a solution or not

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter 7.4, Problem 53E

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To solve: The system of equations {5y2−x2=1xy=2.

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Chapter 7.4, Problem 52E

Chapter 7.4, Problem 54E

Chapter 7 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 7.1 - In Exercises 16, match the equation with one of...Ch. 7.1 - Prob. 2E Ch. 7.1 - In Exercises 16, match the equation with one of...Ch. 7.1 - In Exercises 16, match the equation with one of...Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Find the vertex, the focus, and the directrix....

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Prob. 19E Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Prob. 21E Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 29E Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Flashlight Mirror. A heavy-duty flashlight mirror...Ch. 7.1 - Ultrasound Receiver. Information Unlimited...Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Consider the following linear equations. Without...Ch. 7.1 - Consider the following linear equations. Without...Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Consider the following linear equations. Without...Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Suspension Bridge. The cables of a 200-ft portion...Ch. 7.2 - In Exercises 16, match the equation with one of...Ch. 7.2 - Prob. 2E Ch. 7.2 - Prob. 3E Ch. 7.2 - In Exercises 16, match the equation with one of...Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - Prob. 9E Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Find the vertices and the foci of the ellipse with...Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Find an equation of an ellipse satisfying the...Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Find an equation of an ellipse satisfying the...Ch. 7.2 - Find the center, the vertices, and the foci of the...Ch. 7.2 - Prob. 38E Ch. 7.2 - Find the center, the vertices, and the foci of the...Ch. 7.2 - Find the center, the vertices, and the foci of the...Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.2 - Prob. 48E Ch. 7.2 - Prob. 49E Ch. 7.2 - Prob. 50E Ch. 7.2 - Prob. 51E Ch. 7.2 - Prob. 52E Ch. 7.2 - Prob. 53E Ch. 7.2 - Prob. 54E Ch. 7.2 - Prob. 55E Ch. 7.2 - Prob. 56E Ch. 7.2 - Prob. 57E Ch. 7.2 - Prob. 58E Ch. 7.2 - Prob. 59E Ch. 7.2 - Prob. 60E Ch. 7.2 - Prob. 61E Ch. 7.2 - Prob. 62E Ch. 7.2 - Prob. 63E Ch. 7.2 - Prob. 64E Ch. 7.2 - Prob. 65E Ch. 7.2 - Prob. 66E Ch. 7.2 - Prob. 67E Ch. 7.2 - Find an equation of an ellipse satisfying the...Ch. 7.2 - Bridge Arch. A bridge with a semielliptical arch...Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Find the center, the vertices, the foci, and the...Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Solve. [6.1], [6.3], [6.5], [6.6] 3x + 2y = 1, 2x...Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 53E Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - Solve. x2+y2+6y+5=0,x2+y22x8=0 Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 42E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - Prob. 47E Ch. 7.4 - Prob. 48E Ch. 7.4 - Prob. 49E Ch. 7.4 - Prob. 50E Ch. 7.4 - Prob. 51E Ch. 7.4 - Prob. 52E Ch. 7.4 - Prob. 53E Ch. 7.4 - Prob. 54E Ch. 7.4 - Prob. 55E Ch. 7.4 - Prob. 56E Ch. 7.4 - In Exercises 5558, determine whether the statement...Ch. 7.4 - Prob. 58E Ch. 7.4 - Prob. 59E Ch. 7.4 - Prob. 60E Ch. 7.4 - Prob. 61E Ch. 7.4 - Prob. 62E Ch. 7.4 - Prob. 63E Ch. 7.4 - Prob. 64E Ch. 7.4 - Prob. 65E Ch. 7.4 - Prob. 66E Ch. 7.4 - Prob. 67E Ch. 7.4 - Prob. 68E Ch. 7.4 - Prob. 69E Ch. 7.4 - Prob. 70E Ch. 7.4 - Prob. 71E Ch. 7.4 - Prob. 72E Ch. 7.4 - Prob. 73E Ch. 7.4 - Prob. 74E Ch. 7.4 - Prob. 75E Ch. 7.4 - Prob. 76E Ch. 7.4 - Graph the system of inequalities. Then find the...Ch. 7.4 - Prob. 78E Ch. 7.4 - Prob. 79E Ch. 7.4 - Graph the system of inequalities. Then find the...Ch. 7.4 - Graph the system of inequalities. Then find the...Ch. 7.4 - Prob. 82E Ch. 7.4 - Prob. 83E Ch. 7.4 - Prob. 84E Ch. 7.4 - Prob. 85E Ch. 7.4 - Prob. 86E Ch. 7.4 - Prob. 87E Ch. 7.4 - Prob. 88E Ch. 7.4 - Prob. 89E Ch. 7.4 - Prob. 90E Ch. 7.4 - Find an equation of an ellipse centered at the...Ch. 7.4 - Prob. 92E Ch. 7.4 - Prob. 93E Ch. 7.4 - Prob. 94E Ch. 7.4 - Prob. 95E Ch. 7.4 - Prob. 96E Ch. 7.4 - Prob. 97E Ch. 7.4 - Prob. 98E Ch. 7.4 - Prob. 99E Ch. 7.4 - Prob. 100E Ch. 7.4 - Prob. 101E Ch. 7.4 - Prob. 102E Ch. 7.4 - Prob. 103E Ch. 7.4 - Prob. 104E Ch. 7.4 - Prob. 105E Ch. 7.4 - Prob. 106E Ch. 7.4 - Prob. 107E Ch. 7.4 - Prob. 108E Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 3MC Ch. 7 - Determine whether the statement is true or false....Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - In Exercises 512, match the equation with one of...Ch. 7 - Find the vertex, the focus, and the directrix of...Ch. 7 - Prob. 14MC Ch. 7 - Prob. 15MC Ch. 7 - Prob. 16MC Ch. 7 - Prob. 17MC Ch. 7 - Prob. 18MC Ch. 7 - Prob. 19MC Ch. 7 - Prob. 20MC Ch. 7 - Prob. 21MC Ch. 7 - Prob. 22MC Ch. 7 - Prob. 23MC Ch. 7 - Prob. 24MC Ch. 7 - Prob. 25MC Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Graph the system of inequalities. Then find the...Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Navigation. Two radio transmitters positioned 400...Ch. 7 - Prob. 1T Ch. 7 - Prob. 2T Ch. 7 - Prob. 3T Ch. 7 - Prob. 4T Ch. 7 - Prob. 5T Ch. 7 - Prob. 6T Ch. 7 - Prob. 7T Ch. 7 - Prob. 8T Ch. 7 - Prob. 9T Ch. 7 - Prob. 10T Ch. 7 - Prob. 11T Ch. 7 - Prob. 12T Ch. 7 - Prob. 13T Ch. 7 - Prob. 14T Ch. 7 - Prob. 15T Ch. 7 - Prob. 16T Ch. 7 - Prob. 17T Ch. 7 - Prob. 18T Ch. 7 - Prob. 19T Ch. 7 - Prob. 20T Ch. 7 - Graph the system of inequalities. Then find the...Ch. 7 - Prob. 22T Ch. 7 - Prob. 23T

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The system of equations { 5 y 2 − x 2 = 1 x y = 2 .

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To solve: The system of equations {5y2−x2=1xy=2.

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Chapter 7 Solutions