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.
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☛ 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.
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