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Question
If a pair of linear equations is consistent, then the lines representing them are either _______ or ________.
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Solution
If a pair of linear equations is consistent, then two case arises:
Case 1: When the lines are coincident, they have infinitely many solutions.
Case 2: When the lines are intersecting, they have a unique solution.
Hence, If a pair of linear equations is consistent, then the lines representing them are either coincident or intersecting.
Case 1: When the lines are coincident, they have infinitely many solutions.
Case 2: When the lines are intersecting, they have a unique solution.
Hence, If a pair of linear equations is consistent, then the lines representing them are either coincident or intersecting.
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