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
∴