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Question
The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is ______.
Options
3
– 3
–12
No value
Solution
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.
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