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Q2.

Expert-verifiedFound in: Page 388

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**

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.

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.

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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