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The value of c for which the pair of equations (linear) cx-y=2 and 6x-2y-y=0 will have infinitely many solutions is: 
A) 3  B) -3  C) -12  D) 12
Thank you <3

Dear student,
Your question is bit wrong as the second equation have 6x-2y-y=0. But I am assuming it to be as 6x-2y-4=0. The solution to this question is given below:

The correct answer is option - a

If this is not the question you intended to ask, please re-post this question again with correct equation so that we can provide you with some meaningful help. Looking forward to hear from you again.

Regards

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Dear student,

D. no value

Condition for infinitely many solutions

a1/a2 = b1/b2≠ c1/c2 …(i)

 

The given lines are cx - y - 2 = 0 and 6x - 2y - 3 = 0;

 

Comparing with ax + by + c = 0;

 

Here, a1 = c, b1 = - 1, c1 = - 2

 

and a2 = 6, b2 = - 2,c2 = - 3

 

From Eq. (i),

 

Here, c/6 = -1/- 2

 

Also c/6 = -2/- 3

 

Solving, we get, c = 3 and c = 4.

 

Since, c has different values and so it’s not possible.

 

Hence, for no value of c the pair of equations will have infinitely many solutions.

Regards

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