.Assertion: When $k = − 4$ , then linear equations $x + (k + 1) y = 5, (k + 1) x + 9 y = 8 k − 1$ have infinitely many solutions.

Reason $a 1 x + b 1 y + c 1 = 0$ and $a 2 x + b 2 y + c 2 = 0$ have infinitely many solutions of $a 1 a 2 = b 1 b 2 = c 1 c 2$

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Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

Assertion is correct but Reason is incorrect.

Assertion is incorrect but Reason is correct.

answer is D.

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Detailed Solution

Consistent refers to a unique solution or infinite solution
Condition for a consistent or dependent pair of linear equations

∵ 1 k + 1 = k + 1 9 = 5 8 k − 1 ⇒ k = − 4 ∴ a 1 a 2 = b 1 b 2 = c 1 c 2 [infinitesolution]

Therefore, the assertion is incorrect, and Reason is correct
Hence, option (4) is correct.

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