Q. 175.0( 3 Votes )

# 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).

Answer :

Given: kx + 3y = (2k + 1) – eq 1

2(k + 1)x + 9y = (7k + 1) – eq 2

Here,

a_{1} = k, b_{1} = 3, c_{1} = - (2k + 1)

a_{2} = 2(k + 1) , b_{2} = 9 , c_{2} = - (7k + 1)

Given that system of equations has infinitely many solution

∴ = =

= =

Here,

=

9k = 6×(k + 1)

9k = 6k + 6

9K – 6k = 6

3k = 6

K =

K = 2

∴ k = 2

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