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Q2.

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Algebra 1

Found in: Page 388

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

**State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

If a consistent system as exactly two solution(s), it is said to be independent.**

The given statement is false and the corrected statement is “If a consistent system as exactly one solution, it is said to be independent.”.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the concept of consistent and inconsistent solution.

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

If a system has at exactly one solution, more than one solution or infinitely many solutions, then it is said to be consistent.
If a system of equations has no solution, then it is said to be inconsistent.

Step 2. State the concept of independent and dependent solution.

If a consistent system has exactly one solution, it is independent and if a consistent system has an infinite number of solutions, it is dependent.

Step 3. State the conclusion.

Since, a system of two linear equations is independent if it has exactly one solution, therefore, the given statement “If a consistent system as exactly two solution(s), it is said to be independent” is false. The corrected statement will be:

If a consistent system as exactly one solution, it is said to be independent.

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