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Question

Assertion :x+y4=0 and 2x+ky3=0 has no solution if k=2 Reason: a1x+b1y+c1=0 and a2x+b2y+c2=0 are consistent if a1a2b1b2

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Forthelinestobeparallela1a2=b1b2c1c2.Theequationsarex+y4=0and2x+ky3=0.Herea1=1,b1=1andc1=4.a2=2,b2=kandc2=3.a1a2=12,b1b2=1k,c1c2=43=43.So1k=12k=2Sotheassertioniscorrect.Butwhena1a2b1b2,theequationhasauniquesolution.So,thesystemisconsistent.Sothisreasonistrue.Thereasondoesnotexplaintheassertioncorrectly.AnsOptionB.

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