Question

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

Answer 1

No.

The given pair of linear equations

λx + 3y + 7 = 0 and 2x + 6y - 14 = 0.

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

Here, a1 = λ, b1 = 3, c1 = 7;

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

a1 /a2 = λ /2

b1 /b2 = 1/2

c1 /c2 = - 1/2

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

So λ /2 = 1/2

λ = 1

Also λ /2 = - 1/2

λ = -1

Since,λ does not have a unique value. So, for no value of λ, the given pair of linear equations has infinitely many solutions.