Explanation Procedure used: Solving linear systems by Substitution: “(1) Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step). (2) Substitute the expression found in step 1 into the other equation. (3) Solve the equation containing one variable. (4) Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable. (5) Check the proposed solution in both of the system’s given equations.” Calculation: Consider the given equations. 0.4 x − 2.5 y = − 6.5 (1) x + y = 5.5 (2) In the equation (2), convert the variable x in terms of y . x + y = 5.5 x = 5.5 − y Substitute 5.5 − y for x in the equation (1), 0.4 ( 5.5 − y ) − 2.5 y = − 6.5 Here, the variable x is eliminated and solve the equation as follows. 0.4 ( 5.5 − y ) − 2.5 y = − 6.5 2.2 − 0.4 y − 2.5 y = − 6.5 − 2.9 y = − 6.5 − 2.2 y = − 8.7 − 2.9 On further simplification gives, y = 8.7 2.9 y = 3 Now, substitute 3 for y in one of the given equation and obtain the value of x . x = 5.5 − y x = 5.5 − 3 x = 2.5 Thus, the required solution is ( 2.5 , 3 ) . Check whether the obtained solution ( 2.5 , 3 ) satisfies the given equations or not. Replace variable x with 2.5 and variable y with 3 , in the equation (1). 0

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter 4, Problem 12T

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To solve: The system of linear equations 0.4x−2.5y=−6.5 and x+y=5.5.

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Chapter 4, Problem 11T

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Chapter 4 Solutions

Elementary & Intermediate Algebra

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The system of linear equations 0.4 x − 2.5 y = − 6.5 and x + y = 5.5 .

Solution Summary: The author explains how to solve the system of linear equations by substitution.

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To solve: The system of linear equations 0.4x−2.5y=−6.5 and x+y=5.5.

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Chapter 4 Solutions