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

2x + (k – 2)y = k,

6x + (2k – 1)y = (2k + 5).

Given: 2x + (k – 2)y = k – eq 1

6x + (2k – 1)y = (2k + 5) – eq 2

Here,

a₁ = 2, b₁ = k – 2, c₁ = k

a₂ = 6 , b₂ = 2k – 1, c₂ = 2k + 5

Given that system of equations has infinitely many solution

∴ = =

= =

Here,

=

2×(2k – 1) = 6×(k - 2)

4k – 2 = 6k – 12

12 – 2 = 6k – 4k

2k = 10

K = 5

∴ k = 5