The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is

Condition for infinitely many solutions

a_{1}/a_{2} = b_{1}/b_{2} c_{1}/c_{2} …(i)

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

Comparing with ax + by + c = 0;

Here, a_{1} = c, b_{1} = - 1, c_{1} = - 2

and a_{2} = 6, b_{2} = - 2,c_{2} = - 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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