find the va

We have,

2x + 3y = 7

⇒ 2x + 3y – 7 = 0 ….. (1)

(k+1)x + (2k-1)y = 4k + 1

⇒ (k +1)x + (2k – 1)y – (4k+1) = 0 ….. (2)

For the equations of the form:

a₁x+ b₁ y + c₁ = 0

a₂ x+ b₂y + c₂ = 0

The condition for having infinitely many solutions is:

For the equations (1) and (2),

Now,

2(2k-1) = 3(k+1)

⇒ 4k – 2 = 3k + 3

⇒ k = 5

or

2(4k+1) = 7(k+1)

⇒ 8k + 2 = 7k + 7

⇒ k = 5

Hence, the value k =5 will give infinitely many solutions for the given set of equations.