Question

Question 8
The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(A) 3
(B) – 3
(C) –12
(D) no value

Answer 1

Answer - D

Condition for infinitely many solutions
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
The given lines are cx – y = 2 and 6x – 2y = 3
$Here,a_1=c,b_1=-1,c_1=-2and{a}_2=6b_2=-2,c_2=-3$
$fromeq.\left(i\right).\frac{c}{6}=\frac{-1}{-2}=\frac{-2}{-3}$

$\Rightarrow \frac{c}{6}=\frac{1}{2}and\frac{c}{6}=\frac{2}{3}\Rightarrow c=3andc=4$

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.