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

2x + 3y = 7,


(k - 1)x + (k + 2)y = 3k.

Given: 2x + 3y = 7 – eq 1


(k - 1)x + (k + 2)y = 3k – eq 2


Here,


a1 = 2, b1 = 3, c1 = 7


a2 = k - 1, b2 = k + 2, c2 = 3k


Given that system of equations has infinitely many solution


∴ = =


= =


Here,


=


2×(k + 2) = 3×(k - 1)


2k + 4 = 3k – 3


3k – 2k = 4 + 3


K = 7


∴ k = 7


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