Explanation Formula used: Addition method is used to solve the linear system of equations as well as nonlinear system of equations for one or more variables in which the two equations are added together to eliminate one variable. Calculation: Consider the system of equations, 2 x 2 − 3 y 2 = 5 …… (1) 3 x 2 + 4 y 2 = 16 …… (2) Multiply equation (1) by 4, equation (2) by 3 and add them together, 8 x 2 − 12 y 2 = 20 9 x 2 + 12 y 2 = 48 _ 17 x 2 = 68 This gives, 17 x 2 = 68 x 2 = 68 17 x 2 = 4 x = ± 2 Therefore, x = 2 or − 2 If x = 2 , then x 2 = 4 . Substitute this value into equation (2) gives, 3 x 2 + 4 y 2 = 16 3 ( 4 ) + 4 y 2 = 16 12 + 4 y 2 = 16 4 y 2 = 16 − 12 Further solving, 4 y 2 = 16 − 12 4 y 2 = 4 y 2 = 1 y = ± 1 Similarly, if x = − 2 , then y = ± 1 . Thus, the solutions of the system are ( 2 , 1 ) , ( 2 , − 1 ) , ( − 2 , 1 ) and ( − 2 , − 1 )

8th Edition

ISBN: 9780134178967

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 9.5, Problem 14E

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To calculate: The solution of the following system by the addition method and verify it by plotting a graph of each equations,

2x2−3y2=53x2+4y2=16

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Chapter 9.5, Problem 13E

Chapter 9.5, Problem 15E

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Chapter 9 Solutions

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The solution of the following system by the addition method and verify it by plotting a graph of each equations, 2 x 2 − 3 y 2 = 5 3 x 2 + 4 y 2 = 16

Solution Summary: The author explains the addition method used to solve the linear and nonlinear systems of equations.

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To calculate: The solution of the following system by the addition method and verify it by plotting a graph of each equations,

2x2−3y2=53x2+4y2=16

Want to see the full answer?

Chapter 9 Solutions

The solution of the following system by the addition method and verify it by plotting a graph of each equations, 2 x 2 − 3 y 2 = 5 3 x 2 + 4 y 2 = 16

Solution Summary: The author explains the addition method used to solve the linear and nonlinear systems of equations.

Videos

To calculate: The solution of the following system by the addition method and verify it by plotting a graph of each equations, 2x2−3y2=53x2+4y2=16

Want to see the full answer?

Chapter 9 Solutions

To calculate: The solution of the following system by the addition method and verify it by plotting a graph of each equations,

2x2−3y2=53x2+4y2=16