Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

kx + 3y = (2k + 1),


2(k + 1)x + 9y = (7k + 1).

Given: kx + 3y = (2k + 1) – eq 1


2(k + 1)x + 9y = (7k + 1) – eq 2


Here,


a1 = k, b1 = 3, c1 = - (2k + 1)


a2 = 2(k + 1) , b2 = 9 , c2 = - (7k + 1)


Given that system of equations has infinitely many solution


∴ = =


= =


Here,


=


9k = 6×(k + 1)


9k = 6k + 6


9K – 6k = 6


3k = 6


K =


K = 2


∴ k = 2


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