Find the values of a&b   for which the following pair of linear equations has infinitely many solutions. 2x+y−5=0 (a+b)x+(5a−7b)y−20=0

# Find the values of   for which the following pair of linear equations has infinitely many solutions.

1. A
a = 5 and b = -3
2. B
a = 5 and b = 3
3. C
a = -5 and b = 3
4. D
a = -5 and b = -3

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### Solution:

Given pair of linear equations   and   has infinite number of solutions. We need to find the value of  .
A system of linear equations   and   will have infinite solutions when  .
Now from   and  , we have,
and
Now, substituting the values in the condition we have,

On comparing, we have,

And,

Multiply equation (i), by 7, we have,

Now adding the above equation to equation (ii),

Now, substituting the value of   in equation (i), we have,

Thus, the value of   is 5 and the value of   is 3.
Therefore, option 2 is correct.

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