For what value of k does the system of equations

kx + 2y = 5, 3x – 4y = 10


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

(i) Given: kx + 2y = 5 – eq 1


3x – 4y = 10 – eq 2


Here,


a1 = k, b1 = 2, c1 = 5


a2 = 3, b2 = - 4, c2 = 10


Given systems of equations has a unique solution




- 4k 6


k


k


(ii) Given: kx + 2y = 5 – eq 1


3x – 4y = 10 – eq 2


Here,


a1 = k, b1 = 2, c1 = 5


a2 = 3, b2 = - 4, c2 = 10


Given that systems of equations has no solution


=


Here,


=


Here,


- 4k = 6



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