Given:

Equation 1: 2x - 3y = 7

Equation 2: (k + 1)x + (1 - 2k)y = (5k - 4)

Both the equations are in the form of :

a₁x + b₁y = c₁ & a₂x + b₂y = c₂ where

For the system of linear equations to have infinitely many solutions, we must have

………(i)

According to the problem:

a₁ = 2

a₂ = k + 1

b₁ = -3

b₂ = 1-2k

c₁ = 7

c₂ = 5k-4

Putting the above values in equation (i) we get:

⇒ 2(1-2k) = -3(k + 1)

⇒ 2-4k = -3k-3

⇒ k = 5

The value of k for which the system of equations has infinitely many solutions is k = 5