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