Question

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

पर्याय

• 3

• – 3

• –12

• No value

Answer 1

The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is no value.

Explanation:

The given equations of lines are cx – y = 2 and 6x – 2y = 3

⇒ cx – y – 2 = 0 and 6x – 2y – 3 = 0

Here, a₁ = c

b₁= –1

c₁ = –2

And a₂ = 6

b₂ = –2

c₂ = –3

Since, condition for infinitely many solutions is

`a_1/a_2 = b_1/b_2 = c_1/c_2`

⇒ `c/6 = (-1)/(-2) = (-2)/(-3)`

⇒ `c/6 = 1/2` and `c/6 = 2/3`

⇒ c = 3 and c = 4

Since, c has different values.

So, there exists no value of c for which given equations have infinitely many solutions.