Question 8
The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(A) 3
(B) – 3
(C) –12
(D) no value

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Solution

Condition for infinitely many solutions
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
The given lines are cx – y = 2 and 6x – 2y = 3
$H e r e, a_{1} = 6, b_{2} = - x, c_{2} = - 3 a n d a_{1} = 6 b_{2} = - 2, c_{2} = - 3$
$f r o m e q . (i) . \frac{c}{6} = \frac{- 1}{- 2} = \frac{- 2}{- 3} h e r e, \frac{c}{6} = \frac{1}{2} a n d \frac{c}{6} = \frac{2}{3} \Rightarrow c = 3 a n d c = 4$
Since, c has different values
Hence, for no value of c the pair of equations will have infinitely many solutions.

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Question 8
The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
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Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value

Question 8
The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(A) 3
(B) – 3
(C) –12
(D) no value