The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(B) – 3
(D) no value
Answer - D
Condition for infinitely many solutions
The given lines are cx – y = 2 and 6x – 2y = 3
Here, a1=c, b1=−1, c1=−2and a2=6 b2=−2, c2=−3
from eq.(i). c6=−1−2=−2−3
⇒c6=12 and c6=23⇒ c=3 and c=4
c has two different values when two different relations are considered.
Hence, for no value of c the pair of equations will have infinitely many solutions.