Question

K के किस मान के लिए दिये गये समीकरण निकाय 5x - 7y - 5 = 0 और 2x + ky - 1 = 0 का अद्वितीय हल होगा।​

Answer 1

For which value of K will the unique solution of the given equation be 5x - 7y - 5 = 0 and 2x + ky - 1 = 0.

$\underline{\textsf{Given:}}$

$\mathsf{5x-7y-5=0}$

$\mathsf{2x+ky-1=0}$

$\underline{\textsf{To find:}}$

$\textsf{The value of k for which the equations have unique solution}$

$\underline{\textsf{Solution:}}$

$\underliene{\textsf{Concept used:}}$

$\textsf{The equations}$

$\mathsf{a_1x+b_1y+c_1=0,\;\;a_2x+b_2y+c_2=0}$

$\textsf{have unique solution if}\;\;\mathsf{a_1b_2-a_2b_1\,{\neq}\,0}$

$\textsf{The given equations have unique solution if}$

$\mathsf{5k-2(-7)\,{\neq}\,0}$

$\mathsf{5k+14\,{\neq}\,0}$

$\mathsf{5k\,{\neq}\,-14}$

$\mathsf{k\,{\neq}\,\dfrac{-14}{5}}$

$\underline{\textsf{Answer:}}$

$\textsf{The given equations have unique solution only when}\;\mathsf{k\,{\neq}\,\dfrac{-14}{5}}$