For what value of k does the system of equations

x + 2y = 5, 3x + ky + 15 = 0


have (i) a unique solution, (ii) no solution?

(i) Given: x + 2y = 5 – eq 1


3x + ky + 15 = 0 – eq 2


Here,


a1 = 1, b1 = 2, c1 = - 5


a2 = 3, b2 = k, c2 = 15


Given systems of equations has a unique solution


∴ ≠


≠


k ≠6


∴ k ≠ 6


(ii) Given: x + 2y = 5 – eq 1


3x + ky + 15 = 0 – eq 2


Here,


a1 = 1, b1 = 2, c1 = - 5


a2 = 3, b2 = k, c2 = 15


Given that systems of equations has no solution


∴ = ≠


Here,


=


Here,


k = 6


∴ k = 6


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