pair of linear equations x + 3y -6=0 and x+ ky – 15 =0 has a unique solution if k is​

1 thought on “pair of linear equations x + 3y -6=0 and x+ ky – 15 =0 has a unique solution if k is​”

1. Given Equation

   ⇒x + 3y – 6 = 0 (i)

   ⇒x + ky – 15 = 0 (ii)

   Now compare With

   ⇒ax + by – c = 0

   We get

   ⇒a₁ = 1 , b₁=3 and c₁ = -6

   ⇒a₂ = 1 ,b₂ = k and c₂ = -15

   For Unique Solution

   ⇒a₁/a₂ ≠b₁/b₂

   ⇒1/1 ≠ 3/k

   ⇒k≠3

   Answer

   ⇒k≠3

   More Information

   For Unique Solution

   ⇒a₁/a₂ ≠b₁/b₂

   For Infinite Solution

   ⇒a₁/a₂ = b₁/b₂ = c₁/c₂

   For No Solution

   ⇒a₁/a₂ = b₁/b₂ ≠ c₁/c₂

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