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

5x + 2y = 2k,


2(k + 1)x + ky = (3k + 4).

Given: 5x + 2y = 2k – eq 1


2(k + 1)x + ky = (3k + 4) – eq 2


Here,


a1 = 5, b1 = 2, c1 = - 2k


a2 = 2(k + 1) , b2 = k, c2 = - (3k + 4)


Given that system of equations has infinitely many solution


∴ = =


= =


Here,


=


5k = 4×(k + 1)


5k = 4k + 4


5K – 4k = 4


k = 4


∴ k = 4


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