For what value of a and b, the following equations have infinitely many solutions.

2x + 3y - 7 = 0

(a-b)x + (a+b)y - 3a - b +2  = 0.

 

Dear student,
Cross multiplication method is being used in the solution.
 
The given system of equations is
 
 
 
When b = 1, we get
 
a = 5 × (1) = 5  ( a = 5b )
 
Thus, the value of a and b is 5 and 1 respectively.
 
Cheers!

 

  • 8

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

2(a+b)=3(a-b)

2a+2b=3a-3b

a=5b

also, 2(3a+b-2)=7(a+b)

6a+2b-4=7a+7b

a=-5b-4

=>5b=-5b-4

10b=-4

b=-2/5 and a=-2

  • 4

 The values are

a = 5, b = 1.

  • -2
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