Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Matrices
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Chapter 3, Problem 5MCQ
To determine

To explain: The type of system shown by given system of equations.

  2x+4y=53x+6y=11

A. consistent and dependent

B. consistent and independent

C. inconsistent

D. none of the above

Expert Solution & Answer
Check Mark

Answer to Problem 5MCQ

The system of equations is inconsistent. Option C. is correct.

Explanation of Solution

Given information:

The system of equations

  2x+4y=53x+6y=11

Formula used:

A system of equation is said to be consistent if it has at least one solution.

A consistent system is said to be dependent if it has an infinite number of solutions and graph of both the equations represents the same line.

A consistent system is said to be independent if it has exactly one solution and graph of both the equations cut at only one point.

A system of equation is said to be inconsistent if it has no solution and graph of both the equations represents two parallel lines.

Calculation:

Consider the system of equations

  2x+4y=53x+6y=11

Multiply first equation by 3 and second equation by −2 and then add both the equations.

  2x+4y=53(2x+4y)=3(5)6x+12y=15

  3x+6y=11−2(3x+6y)=(−2)(11)−6x−12y=−22

Now, add both the equations as,

  6x+12y=15−6x−12y=−22+0+0=−7

Since, 0=−7 is not possible; the given system of equations has no solution.

Recall that a system of equation is said to be inconsistent if it has no solution and graph of both the equations represents two parallel lines.

Therefore, the given system of equations has no solution and is inconsistent.

Thus, the system of equations is inconsistent. Option C. is correct.

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Chapter 3, Problem 4MCQ
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Chapter 3, Problem 6MCQ

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
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