Answer :

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.

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