Find the values of A and B for which the following pair of linear equations infinitely many solutions:

2x+3y=7

(a+b)x+(2a-b)y=21

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Solution

Note:For the equations to have infinite solution

2/(a+b) = 3/(2a-b) = 7/21

So

2/(a+b) = 7/21=1/3

Cross multiplying

a+b = 6 ----->(1)

3/(2a-b) = 7/21=1/3

Cross multiplying

2a-b= 9 ---->(2)

Adding (1) & (2)

We get

3a=15

So a=15/3=5

Putting it in (1)

a+b=5+b=6

So b=6-5=1

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Similar questions

2 x + 3 y = 7 (a + b) x + (2 a - b) y = 21

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations:

$2 x + 3 y = 7, (a + b) x + (2 a - b) y = 21.$

2 x + 3 y = 7

(a + b) x + (2 a - b) y = 21

(i) For which values of a and b will the following pair of linear equations have an

infinite number of solutions?

(ii) For which value of k will the following pair of linear equations have no solution?

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