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


No.

The given pair of linear equations


and 2x + 6y - 14 = 0.


Here, Comparing with ax + by + c = 0;


Here, a1 = , b1 = 3, c1 = 7;


And a2 = 2, b2 = 6, c2 = - 14;


a1 /a2 = /2


b1 /b2 = 1/2


c1 /c2 = - 1/2


If a1/a2 = b1/b2 = c1/c2, then system has infinitely many solutions.


So /2 = 1/2


= 1


Also /2 = - 1/2



Since, does not have a unique value.


So, for no value of, the given pair of linear equations has infinitely many solutions.


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