Question

For which value of k will the following pair of
linear equations have an infinite numbekr of
solutions ?
(i) 2x + 3y = 7
(a - b)x + (a + b)y = 3a + b - 2
​

Answer 1

Answer:

2x+3y=7

(a−b)x+(a+b)y=3a+b−2

∵ It has infinitely many solutions.  

∴  

a  

2

​  

 

a  

1

​  

 

​  

=  

b  

2

​  

 

b  

1

​  

 

​  

=  

c  

2

​  

 

c  

1

​  

 

​  

 

(i)

a−b

2

​  

 

​  

=  

(ii)

a+b

3

​  

 

​  

=  

(iii)

3a+b−2

7

​  

 

​  

 

From (i) and (ii)

a+b

3

​  

=  

3a+b−2

7

​  

 

7a+7b=9a+3b−6

⇒2a−4b=6

⇒a−2b=3

⇒5b−2b=3

⇒3b=3⇒b=1

∴a=5×1=5.

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