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

MyLab Math with Pearson eText -- 24 MonthStandalone Access Card -- for Intermediate Algebra with Integrated Review

8th Edition

ISBN: 9780135910023

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

Publisher: PEARSON

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Chapter 9.5, Problem 2E

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

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Chapter 9.5, Problem 1E

Chapter 9.5, Problem 3E

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MyLab Math with Pearson eText -- 24 MonthStandalone Access Card -- for Intermediate Algebra with Integrated Review

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

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Chapter 9 Solutions