Question

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

Answer 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