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

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-3

-12

No value

answer is A.

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Detailed Solution

Given pair of linear equations are,

cx - y = 2

… (1)

6 x - 2 y = 3

… (2)
Given pair of linear equations have no solution.
On comparing the given pair of linear equations with

ax + by + c = 0

we get,

a_{1} = c, b_{1} = - 1, c_{1} = - 2

a_{2} = 6, b_{2} = - 2, c_{2} = - 3

Then,

\frac{a_{1}}{a_{2}} = \frac{c}{6}

\frac{b_{1}}{b_{2}} = \frac{1}{2}

\frac{c_{1}}{c_{2}} = \frac{2}{3}

We know that for infinitely many solutions of the pair of linear equations,

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

⇒ c 6 = 12 = 23

We will first take the first and second ratios.

⇒ c 6 = 12 ∴ c = 3

Now, we will take the first and third ratio

⇒ c 6 = 23 ∴ c = 4

It is not possible that c has two values.
Therefore, option 4 is correct.

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