Explanation Given Information: The provided system of equations is, 2 x + 3 y = − 2 2 x − y = 9 Formula used: Multiplication property of equality: A = B and A ⋅ C = B ⋅ C are equivalent where C ≠ 0 . If A , B and C are real numbers then, Addition property of equality: A = B and A + C = B + C are equivalent. Calculation: Consider the system of equations: 2 x + 3 y = − 2 …… (1) 2 x − y = 9 …… (2) Since, coefficient of y is 1 in the equation ( 2 ) Use addition property, Add ( − 2 x ) to both sides of the equation ( 2 ) Thus, − 2 x + 2 x − y = 9 − 2 x y = 2 x − 9 Put the value y = 2 x − 9 in equation ( 1 ) Thus, 2 x + 3 ( 2 x − 9 ) = − 2 Remove parentheses, 2 x + 6 x − 27 = − 2 Take like terms together, 8 x − 27 = − 2 Use addition property, Add ( 27 ) to both sides, 8 x − 27 + 27 = − 2 + 27 8 x = 25 Use multiplication property, Multiply both side by ( 1 8 )

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 13.2, Problem 19ES

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To calculate: The solution of equations 2x+3y=−2, 2x−y=9 using substitution method. First solve one equation for one variable.

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Chapter 13.2, Problem 18ES

Chapter 13.2, Problem 20ES

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Chapter 13 Solutions

Developmental Mathematics (9th Edition)

Ch. 13.1 - Prob. 1SR Ch. 13.1 - Prob. 2SR Ch. 13.1 - Prob. 1DE Ch. 13.1 - Prob. 2DE Ch. 13.1 - Prob. 3DE Ch. 13.1 - Prob. 4DE Ch. 13.1 - Prob. 5DE Ch. 13.1 - Prob. 6DE Ch. 13.1 - Prob. 7DE Ch. 13.1 - Prob. 8DE

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The solution of equations 2 x + 3 y = − 2 , 2 x − y = 9 using substitution method. First solve one equation for one variable.

Solution Summary: The author calculates the solution of the equations 2x+3y=-2,2x-y =9 using substitution method.

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To calculate: The solution of equations 2x+3y=−2, 2x−y=9 using substitution method. First solve one equation for one variable.

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Chapter 13 Solutions