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 ? Give reasons.

Explanation

No.
Given equations are
`lambdax + 3y + 7 = 0` and 2x + 6y - 14 = 0
`therefore a_(1) = lambda, b_(1) = 3, c_(1) = 7, a_(2) = 2, b_(2) = 6, c_(2) = - 14`
We know that the system of equations has infinitely many solutions if
`(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))`
`(lambda)/(2) = (3)/(6) = - (7)/(14)`
Now, `(lambda)/(2) = (3)/(6) implies lambda = 1`
and `(lambda)/(2) = - (7)/(14) implies lambda = - 1`, which contradicts the former value of `lambda`.
`therefore` For no value of `lambda`, the given system of equations has infinitely many solutions.