Explanation Given: The systems of equations, x + 2 y = 0 …… (1) x 2 + 4 y 2 = 32 …… (2) Calculation: From equation (1), write y in terms of x , as follows, x + 2 y = 0 2 y = − x Then, y = − x 2 …… (3) Now, use the value of y from equation (3) in (2), x 2 + 4 ( − x 2 ) 2 = 32 x 2 + 4 ( x 2 4 ) = 32 2 x 2 = 32 Further, x 2 = 16 x = 16 Then, it gives, x = − 4 and x = 4 Use, the values of x in (3) and find y . For x = − 4 , y = − x 2 = − ( − 4 ) 2 = 4 2 = 2 For x = 4 , y = − x 2 = − ( 4 ) 2 = − 4 2 = − 2 Therefore, the solutions of the system of equations are ( − 4 , 2 ) and ( 4 , − 2 ) . Graph: For the function, x + 2 y = 0 , which is a straight line with the slope − 1 and y − intercept as ( 0 , 0 ) and x − intercept as ( 0 , 0 ) . Now, consider the function, x 2 + 4 y 2 = 32

8th Edition

ISBN: 9780134178967

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

Publisher: PEARSON

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Chapter 9.5, Problem 3E

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To calculate: The systems of equations, x+2y=0 and x2+4y2=32 with the use of method of substitution and graph the equations and verify the result.

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Chapter 9.5, Problem 2E

Chapter 9.5, Problem 4E

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The systems of equations, x + 2 y = 0 and x 2 + 4 y 2 = 32 with the use of method of substitution and graph the equations and verify the result.

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To calculate: The systems of equations, x+2y=0 and x2+4y2=32 with the use of method of substitution and graph the equations and verify the result.

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Chapter 9 Solutions