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Maths / Linear Equations in Two Variables / Relationship of Coefficients with Number of Solutions
QUESTION
 

Assertion :  3x-4y=7  and 6x-8y=k  have infinite number of solution if  k=14.

Reason :  a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0  have a unique solution if  frac {a_1}{a_2}neq frac {b_1}{b_2}.

OPTIONS
A. 

If both Assertion and Reason are correct and Reason is the correct explanation of Asserion.

B. 

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

C. 

If Assertion is correct but Reason is incorrect.

D. 

If Assertion is incorrect but Reason is correct.

Right Option : B
EXPLANATION
Explain TypeExplanation Content
Text

Assertion :  3x-4y=7  and 6x-8y=k  have infinite number of solution if  k=14.

Reason :  a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0  have a unique solution if  frac {a_1}{a_2}neq frac {b_1}{b_2}.

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

If a1 = 3 ,  b1 = -4 ,  c1 = -7  and a2 = 6 ,  b2 = -8 and  c2 = -k

For infinitely many solutions, large frac{a1}{a2}=frac{b1}{b2}=frac{c1}{c2}

 

large frac{3}{6}=frac{-4}{-8}=frac{-7}{-k}

Also, large frac{3}{6}=frac{-7}{-k}

-3k = 42

k = -14

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