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

Given:

The  pair of equations \( c x-y=2 \) and \( 6 x-2 y=3 \).

To do:

We have to find the value of \( c \) for which the pair of equations \( c x-y=2 \) and \( 6 x-2 y=3 \) will have infinitely many solutions.

Solution:

We know that,

The condition for infinitely many solutions is,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

 \( c x-y-2=0 \) and \( 6 x-2 y-3=0 \)

Here,

$a_1=c, b_1=-1, c_1=-2$

$a_2=6, b_2=-2, c_2=-3$

Therefore,

$\frac{c}{6}=\frac{-1}{-2}=\frac{-2}{-3}$

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

$c=3$ and $c=4$

Here, we have two different values of $c$.

Therefore, there is no value of $c$ for which the given equations will have infinitely many solutions.

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Updated on: 10-Oct-2022

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