Question

if the lines given by 2x +ky=1 and 3x-5y=7 has unique solution, then find the value of k.​

Answer 1

Answer:

value of k is any integer or rational number except -10/3

Step-by-step explanation:

Answer 2

Answer:

$\bigstar{\bold{Value\:of\:k\neq -\dfrac{10}{3} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\rm{Given:}}}}$

A pair of equations:

• 2x + ky = 1
• 3x - 5y = 7

$\Large{\underline{\underline{\rm{To\:Find:}}}}$

• The value of k

$\Large{\underline{\underline{\rm{Solution:}}}}$

➔ Here it is given that the pair of equations have a unique solution

➔ If a pair of equations have a unique solution we know that,

    $\tt{\dfrac{a_1}{b_1}\neq \dfrac{b_1}{b_2}}$

    where a₁ = 2, a₂ = 3, b₁ = k, b₂ = 5

➔ Substitute the data,

    $\tt{\dfrac{2}{3}\neq \dfrac{k}{-5}}$

➔ Cross multiplying we get,

    -5 × 2 ≠ 3k

    -10 ≠ 3k

     k ≠ -10/3

➔ Hence the value of k is not equal to -10.

➔ That is k can take the value of any real number other than -10/3

    $\boxed{\bold{Value\:of\:k\neq -\dfrac{10}{3} }}$

$\Large{\underline{\underline{\rm{Notes:}}}}$

➔ If a pair of equations:

    a₁x + b₁y + c₁ = 0

    a₂x + b₂y + c₂ = 0

➟ has a unique solution and is consistent,

    $\tt{\dfrac{a_1}{b_1}\neq \dfrac{b_1}{b_2}}$

➟ has infinite number of solutions and is consistent

    $\tt{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2} }$

➟ has no solution and is inconsistent,

    $\tt{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2} }$