Explanation Given: The given equations are − 5 y + 5 y = 3 x + 2 ( x − 5 ) − 3 x + 5 4 ( x + y ) − x + y = − 12 Method: (a) Steps to solve a system of two Linear Equations by the Substitution Method. 1. Solve one of the equations for one of its variables. 2. Substitute the expression for the variable found in Step 1 into the other equation. 3. Solve the equation from Step 2 to find the value of one variable. 4. Substitute the value found in Step 3 into any equation containing both variables to find the value of the other variable. 5. Check the proposed solution in the original system. (b). When solving a system of equations by the substitution method, if possible, begin by solving for a variable that has a coefficient of 1 or − 1 to avoid working with time consuming fractions. Calculation: − 5 y + 5 y = 3 x + 2 ( x − 5 ) − 3 x + 5 … ( 1 ) 4 ( x + y ) − x + y = − 12 … ( 2 ) Rewrite the equation ( 1 ) in simplest form. − 5 y + 6 y = 3 x + 2 ( x − 5 ) − 3 x + 5 y = 3 x + 2 x − 10 − 3 x + 5 y = 2 x − 5 Rewrite the equation ( 2 ) in simplest form. 4 ( x + y ) − x + y = − 12 4 x + 4 y − x + y = − 12 3 x + 5 y = − 12 Substitute 2 x − 5 for y in equation ( 2 ) and solve for x . 3 x + 5 y = − 12 3 x + 5 ( 2 x − 5 ) = − 12 3 x + 10 x − 25 = − 12 13 x − 25 = − 12 13 x = 13 x = 1 Substitute 1 for x in equation, y = 2 x − 5 , and solve for y

Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)

5th Edition

ISBN: 9780134707631

Author: Elayn Martin-Gay

Publisher: PEARSON

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Chapter 14.2, Problem 45E

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The solution for given equations using substitution method.

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Chapter 14.2, Problem 44E

Chapter 14.2, Problem 46E

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Chapter 14 Solutions

Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)

Ch. 14.1 - Prob. 1P Ch. 14.1 - Prob. 2P Ch. 14.1 - Prob. 3P Ch. 14.1 - Prob. 4P Ch. 14.1 - Prob. 5P Ch. 14.1 - Prob. 6P Ch. 14.1 - Prob. 7P Ch. 14.1 - Prob. 8P Ch. 14.1 - Prob. 1VRVC Ch. 14.1 - Prob. 2VRVC

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The solution for given equations using substitution method.

To solve: The solution for given equations using substitution method.

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Chapter 14 Solutions

To solve:

The solution for given equations using substitution method.