Q. 18

# 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

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