Answer :

Given: Two equations, 2x – 3y = 7


2x 3y 7 = 0


(a + b) x – (a + b – 3) y = 4a + b


(a + b) x – (a + b – 3) y – (4a + b) = 0


We know that the general form for a pair of linear equations in 2 variables x and y is a1x + b1y + c1 = 0


and a2x + b2y + c2 = 0.


Comparing with above equations,


we have a1 = 2,


b1 = - 3,


c1 = - 7;


a2 = a + b,


b2 = - (a + b – 3),


c2 = - (4a + b)





Since, it is given that the equations have infinite number of solutions, then lines are coincident and



So,


Let us consider


Then, by cross multiplication, 2(a + b – 3) = 3(a + b)


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


a + b + 6 = 0 (1)


Now consider


Then, 3(4a + b) = 7(a + b – 3)


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


5a 4b + 21 = 0 (2)


Solving equations (1) and (2),


5 × (1), (5a + 5b + 30) – (5a – 4b + 21) = 0


9b + 9 = 0


9b = - 9


b = - 1


Substitute b value in (1),


a - 1 + 6 = 0


a + 5 = 0


a = - 5


a = - 5; b = - 1

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