Explanation Given Information: The provided system of equations is as follows: 2 x + 2 y = 2 3 x − y = 1 Formula used: Substitution method: Step 1: Isolate a variable in one of the equations (unless one is already isolated). Step 2: Substitute for that variable in the other equation, using parentheses. Step 3: Solve the equation in which the substitution was made. Step 4: Substitute the solution from step (3) in any of the equations, and solve for the other variable. Step 5: Form an ordered pair and check in the original equations. Calculation: Consider the system of equations 2 x + 2 y = 2 and 3 x − y = 1 , and mark them with (1) and (2) for further reference as below: 2 x + 2 y = 2 …… (1) And 3 x − y = 1 …… (2) Since, in both the equations, no variable is isolated. Isolate any variable from any of the two equations; here isolate y from equation (2) as below: 3 x − y = 1 3 x − y − 3 x = 1 − 3 x y = 3 x − 1 Mark the new equation with new number as below: y = 3 x − 1 …… (3) Substitute the value of y from equation (3) to equation (1) as below: 2 x + 2 y = 2 2 x + 2 ( 3 x − 1 ) = 2 Remove parenthesis by distributive law and solve by combining the like terms as below: 2 x + 2 ( 3 x − 1 ) = 2 2 x + 6 x − 2 = 2 8 x − 2 + 2 = 2 + 2 8 x = 4 Further solve the above equation. 8 x = 4 x = 4 8 x = 1 2 Substitute the value of x in equation (3) and solve for the value of y as below: y = 3 x − 1 y = 3 ( 1 2 ) − 1 y = 3 2 − 1 y = 1 2 Then the values are x = 1 2 and y = 1 2

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

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ISBN: 9780137361847

Author: Marvin Bittinger, David Ellenbogen

Publisher: PEARSON+

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Chapter 8.2, Problem 21ES

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Chapter 8.2, Problem 20ES

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Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

Ch. 8.1 - In 2016, there were 35 species of amphibians in...Ch. 8.1 - 2. Refer to Example 2 . For another necklace, Star...Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 1CYU Ch. 8.1 - Prob. 2CYU Ch. 8.1 - Prob. 3CYU Ch. 8.1 - Prob. 4CYU Ch. 8.1 - Prob. 1ES Ch. 8.1 - Prob. 2ES

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The solution for the system of equations 2 x + 2 y = 2 and 3 x − y = 1 by the substitution method.

Solution Summary: The author calculates the solution for the system of equations 2x+2y=2 and 3x-y =1 by the substitution method.

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To calculate: The solution for the system of equations 2x+2y=2 and 3x−y=1 by the substitution method.

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Chapter 8 Solutions