Q1 of 44 Page 3

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). (CBSE 2000)

Given: 2x + (k – 2)y = k – eq 1


6x + (2k – 1)y = (2k + 5) – eq 2


Here,


a1 = 2, b1 = k – 2, c1 = k


a2 = 6 , b2 = 2k – 1, c2 = 2k + 5


Given that system of equations has infinitely many solution


∴ = =


= =


Here,


=


2×(2k – 1) = 6×(k - 2)


4k – 2 = 6k – 12


12 – 2 = 6k – 4k


2k = 10


K = 5


∴ k = 5

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