Question

Determine the value of K, for each of the following:
(i) 2x + 3y - 5 = 0 and Kx - 6y - 8 = 0 have unique solution
(ii) (K - 3)x + 3y = K and Kx - Ky = 12 hae infinite solutions.
(iii) 2x - Ky + 3 = 0 and 3x + 2y - 1 = 0 have no solutions.​

Answer 1

Answer:

(i) For unique solution

a1/a2 ≠ b1/b2

2/k ≠ 3/-6

2× -6 ≠ 3k

k ≠ -4

(ii)For infinite solutions,

a1/a2 = b1/b2 = c1/c2

b1/b2 = c1/c2

-3/k = k/12

-3× 12 = k²

k² = -36

k = ±6

(iii)For no solutions

a1/a2 = b1/b2 ≠ c1/c2

a1/a2 = b1/b2

2/3 = -k/2

2 × 2 = -3k

k = -4/3