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

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.