To determine To choose: The correct option from the following options if a system of dependent equations containing three variables has the general solution { ( x , y , z ) | x = − z + 4 , y = − 2 z + 5 , z is any real number } then the infinite number of solutions of the system. (a). ( 1 , − 1 , 3 ) (b). ( 0 , 4 , 5 ) (c). ( 4 , − 3 , 0 ) (d). ( − 1 , 5 , 7 ) Explanation Concept: If the lines of the system of equations coincide to each other therefore the system of equations is consistent. The coincident lines overlap to each other and the lines are dependent to each other. There are infinitely many solutions. Calculation: The given solution is { ( x , y , z ) | x = − z + 4 , y = − 2 z + 5 , z is any real number } . Option (a) ( 1 , − 1 , 3 ) Substitute 3 for z in the equation x = − z + 4 to check whether the solution is correct or not. x = − 3 + 4 x = 1 Substitute 3 for z in the equation y = − 2 z + 5 to check whether the solution is correct or not. y = − 2 × 3 + 5 y = − 1 Therefore, the option (a) satisfies the given equations. Thus, the option (a) is correct. Option (b). ( 0 , 4 , 5 ) Substitute 5 for z in the equation x = − z + 4 to check whether the solution is correct or not. x = − 5 + 4 x = − 1 Substitute 5 for z in the equation y = − 2 z + 5 to check whether the solution is correct or not. y = − 2 × 5 + 5 y = − 5 Therefore, the option (b) does not satisfy the given equations. So, the option (b) is incorrect

College Algebra: Concepts Through Functions

4th Edition

ISBN: 9780134775807

Author: Sullivan

Publisher: PEARSON

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Chapter 6.1, Problem 8AYU

To determine

To choose: The correct option from the following options if a system of dependent equations containing three variables has the general solution {(x,y,z)|x=−z+4, y=−2z+5, z is any real number} then the infinite number of solutions of the system.

(a). (1,−1,3)

(b). (0,4,5)

(c). (4,−3,0)

(d). (−1,5,7)

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Chapter 6.1, Problem 7AYU

Chapter 6.1, Problem 9AYU

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Chapter 6 Solutions

College Algebra: Concepts Through Functions

Ch. 6.1 - Prob. 1AYU Ch. 6.1 - Prob. 2AYU Ch. 6.1 - Prob. 3AYU Ch. 6.1 - If a system of equations has one solution, the...Ch. 6.1 - Prob. 5AYU Ch. 6.1 - Prob. 6AYU Ch. 6.1 - Prob. 7AYU Ch. 6.1 - If a system of dependent equations containing...Ch. 6.1 - Prob. 9AYU Ch. 6.1 - In Problems 9–18, verify that the values of the...

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