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One equation of a pair of dependent line...

One equation of a pair of dependent linear equations is `-5x + 7y -2 = 0`. The second equation can be

A

`10x + 14 y + 4 = 0`

B

`-10x - 14y +4 =0`

C

`-10 +14y +4 =0`

D

`10x - 14y + 4 = 0`

Text Solution

Verified by Experts

The correct Answer is:
D
Condition for dependent linear equations
`(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = c_(1)/(c_(2)) = (1)/(k)`
Give equation of line is, `-5x + 7y - 2 = 0`
Here, `" " a_(1) = -5, b_(1) = 7, c_(1) = -2`
From Eq. (i), `" " -(5)/(a_(2)) = (7)/(b_(2)) = - (2)/(c_(2)) = (1)/(k) " " ` [say]
`rArr " " a_(2) = -5k, b_(2) = 7k, c_(2) = -2k`
where, k is any arbitrary constant.
Putting k = 2, then `" " a_(2) = -10 , b_(2) = 14`
and `" " c_(2) = -4`
`:.` The required equation of line becomes
`" " a_(2) x + b_(2) y + c_(2) = 0`
`rArr " " -10x + 14y - 4 = 0`
`rArr " " 10x - 14y + 4 = 0`
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