Q18 of 244 Page 124

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

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).

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

kx + 3y = (2k + 1),

2(k + 1)x + 9y = (7k + 1).

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

(k – 1)x – y = 5,

(k + 1)x + (1 – k)y = (3k + 1) .

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

(k – 3)x + 3y = k,

kx + ky = 12.

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).