.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 $a 1 a 2 = b 1 b 2 = c 1 c 2$

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE