For the pair of equations `lambdax + 3y + 7 = 0` and ` 2x + 6y - 14 = 0`. To have infinitely many solutions, the value of `lambda` should be 1 . Is the statement true ?

Options

A. yes
B. no
C. can not say anything
D. none of these

Answer

B

Explanation

No, the given pair of linear equations
`lambdax + 3y + 7 = 0` and `2x + 6y - 14 = 0`
Here, `" " a_(1) = lambda, b_(1) = 3, c_(1) = 7 , a_(2) = 2, b_(2) = 6, c_(2) = -14`
If `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))` , then system has infinitely many solutions.
`rArr " " (lambda)/(2) = (3)/(6) = - (7)/ (14)`
`:' " " (lambda)/(2) = (3)/(6) rArr lambda = 1`
and `" " (lambda)/(2) = - (7)/(14) rArr lambda = -1`
Hence, `lambda = -1` does not have a unique value.
So, for no value of `lambda` the given pair of linear equations has infinitely many solutions.