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

Options

A. 2
B. -3
C. -12
D. no value

Answer

D

Explanation

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 ` and `6x - 2y = 3`
Here, `" " a_(1) = c, b_(1) = -1, c_(1) = -2`
and `" " a_(2) = 6, b_(2) = -2, c_(2) = -3`
From Eq. (i), `" " (c)/(6) =(-1)/(-2) = (-2)/(-3)`
Here, `" " (c)/(6)=(1)/(2)` and `(c)/(6) =(2)/(3)`
`rArr " " c = 3` and `c = 4`
Since, c has different values.
Hence, for no value of c the pair of equations will have infinitely many solutions .