Question

find tha value of a and b for which following system of eqn kas infinity no. of solution 2x +3y=7 (a+b)x - (a+b-3)y = 4a +b

Answer 1

Hey friend,

Here is your answer,
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2x + 3y = 7

(a+b)x - (a+b-3)y = 4a + b

For infinite solutions : a₁ = b₁ = c₁ 
                                   a₂    b₂    c₂

   2    =      3      =    7   
(a+b)    (a+b-3)    4a+b

  2     =      3    
a+b       a+b-3

2a+2b-6 = 3a+3b

a + b = -6                   -----------------(i)


  2   =    7   
a+b    4a+b

8a+2b = 7a+7b

a = 5b


Put a = 5b in (i)

5b + b = -6

6b = -6

  b = -1


Put b = -1 in (i)

a -1 = -6

a = -5



Ans: a = -5  and b = -1.

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