Answer :

Given: 2x - 3y = 7 – eq 1


(a + b)x - (a + b - 3)y = 4a + b – eq 2


Here,


a1 = 2, b1 = - 3, c1 = - 7


a2 = (a + b), b2 = - (a + b - 3), c2 = - (4a + b)


Given that system of equations has infinitely many solution


= =


= =


Here,


=


- 3×( - 4a + b) = - 7× - (a + b - 3)


12a + 3b = 7a + 7b - 21


12a - 7a = - 3b + 7b - 21


5a = 4b - 21


5a – 4b + 21 = 0 eq 3


Also,


=


2× - (4a + b) = - 7×(a + b)


- 8a – 2b = - 7a – 7b


- 8a + 7a = 2b – 7b


- a = - 5b


a = 5b eq 4


substitute – eq 4 in – eq 3


5(5b) – 4b + 21 = 0


25b – 4b + 21 = 0


21b + 21 = 0


b =


b = - 1


substitute ‘b’ in – eq 4


a = 5( - 1)


a = - 5


a = - 5, b = - 1


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