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, a_{1} = , b_{1} = 3, c_{1} = 7;

And a_{2} = 2, b_{2} = 6, c_{2} = - 14;

a_{1} /a_{2} = /2

b_{1} /b_{2} = 1/2

c_{1} /c_{2} = - 1/2

If a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}, 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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