Explanation Given: Fill in the blank so that the resulting statement is true, "When solving x − 7 y = − 22 ; 5 x + 2 y = 1 by the substitution method, we obtain x = − 1 , so the solution set is ______________" Solving the system of equations in two variables means to find all the solutions of the system. A solution of a system of equations in two variables is an ordered pair that satisfies both equations. If the system of equations in two variables has no solution then that system of linear equation is called inconsistent system and if they have a unique solution or multiple solutions then that type of system of linear equations is called Consistent system. One of the ways to solve the system of linear equations is to graph the equation of each line and find where the two lines intersect. The point at which the two lines intersect is the solution to the system of linear equations. If the two lines do not intersect anywhere then they are parallel lines. These parallel lines have no solution. Other than parallel lines, all other type of lines has solutions. The lines which intersect each other will have a unique solution and the lines which are coinciding have infinitely many solutions. Calculation: Description x − 7 y = − 22 ; 5 x + 2 y = 1 Step 1 : Substitute x = − 1 in first equation x − 7 y = − 22 to find the value of y − 1 − 7 y = − 22 ⇒ − 7 y = − 22 + 1 ⇒ − 7 y = − 21 − 7 y − 7 = − 21 − 7 ⇒ y = 3

Introductory Algebra for College Students (7th Edition)

7th Edition

ISBN: 9780134178059

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 4.2, Problem 2CAVC

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The solution to fill the blank in the statementso that the resulting statement is true. The statement in which we have to fill the blank is "When solving x−7y=−22 ; 5x+2y=1 by the substitution method, we obtain x=−1 , so the solution set is ______________"

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Chapter 4.2, Problem 1CAVC

Chapter 4.2, Problem 3CAVC

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Introductory Algebra for College Students (7th Edition)

Ch. 4.1 - Prob. 1CAVC Ch. 4.1 - Fill in each blank so that the resulting statement...Ch. 4.1 - Prob. 3CAVC Ch. 4.1 - Prob. 4CAVC Ch. 4.1 - Prob. 1ES Ch. 4.1 - Prob. 2ES Ch. 4.1 - Prob. 3ES Ch. 4.1 - In Exercises 1-10, determine whether the given...Ch. 4.1 - Prob. 5ES Ch. 4.1 - Prob. 6ES

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The solution to fill the blank in the statementso that the resulting statement is true. The statement in which we have to fill the blank is "When solving x − 7 y = − 22 ; 5 x + 2 y = 1 by the substitution method, we obtain x = − 1 , so the solution set is ______________"

Solution Summary: The author explains how to solve the system of equations in two variables by filling in the blank.

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The solution to fill the blank in the statementso that the resulting statement is true. The statement in which we have to fill the blank is "When solving x−7y=−22 ; 5x+2y=1 by the substitution method, we obtain x=−1 , so the solution set is ______________"

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Chapter 4 Solutions