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Q2.

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Found in: Page 388

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

# 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 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.

1. If a system has at exactly one solution, more than one solution or infinitely many solutions, then it is said to be consistent.
2. 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.