Find the values of a and b for which each of the following systems of linear equations has an infinite number of solutions:

2x + 3y = 7, 2ax + (a + b)y = 28

Given: 2x + 3y = 7 – eq 1


2ax + (a + b)y = 28 – eq 2


Here,


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


a2 = 2a, b2 = (a + b), c2 = - 28


Given that system of equations has infinitely many solution


= =


= =


Here,


=


3× - 28 = - 7×(a + b)


- 84 = – 7a – 7b


7a + 7b – 84 = 0


a + b – 12 = 0 eq 3


Also,


=


2× - 28 = - 7×2a


– 56 = – 14a


14a = 56


a =


a = 4 eq 4


substitute – eq 4 in – eq 3


4 + b – 12 = 0


a + b – 12 = 0


b – 8 = 0


b = 8


a = 4, b = 8


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