Question

For what value of k, the following pair of linear equations has infinite number of
solutions: (2)
2x + 3y = 7; (k -1)x + (k + 2) y = 3k.

Answer 1

☛ 2x + 3y = 7

On comparing,

a1 = 2 ; b1 = 3 ; c1 = 7

☛ (k - 1)x + (k - 2)y = 3k

On comparing,

a2 = k - 1 ; b2 = (k + 2) ; c2 = 3k

For infinite solutions:

☛ a1/a2 = b1/b2 = c1/c2

➜ a1/a2 = b1/b2

➜ 2 / (k - 1) = 3 / (k + 2)

➜ 2k + 4 = 3k - 3

➜ 3k - 2k = 4 + 3

➜ k = 7

Also,

➜ a1/a2 = c1/c2

➜ 2 / (k - 1) = 7 / 3k

➜ 6k = 7k - 7

➜ 7k - 6k = 7

➜ k = 7

Therefore, Value of k is 7.