State whether the following statement is true or false.

If the solution of a pair of linear equations is consistent, then the two lines could be intersecting or coincident.

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True

False

answer is A.

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Detailed Solution

It is given that the solution of a pair of linear equations is consistent.
If a pair of linear equations has a solution, it is said to be consistent.
The fact that the pair of linear equations is consistent is a given.
Then it has either infinite or unique solutions.
We are aware that a unique solution involves intersecting lines, but an infinite number of solutions implies coincident lines.
Therefore, if the solution of a pair of linear equations is consistent, then the two lines could be intersecting or coincident.
Therefore the given statement is true.
Hence option (1) is correct.

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