Question

if the pair of Linear Equations for given by 3x+2ky=2, and 2x+5y+1=0 represents parallel lines then find the value of k

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The lines 3x+2ky=2 and 2x+5y+1=0 are parallel}$

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

$\textsf{The value of k}$

$\underline{\textbf{Solution:}}$

$\mathsf{Slope\;of\;3x+2k\,y-2=0\;is\;m_1=\dfrac{-3}{2k}}$

$\mathsf{Slope\;of\;2x+5y+1=0\;is\;m_2=\dfrac{-2}{5}}$

$\textbf{Since the lines are parallel, their slopes are equal}$

$\implies\mathsf{m_1=m_2}$

$\implies\mathsf{\dfrac{-3}{2k}=\dfrac{-2}{5}}$

$\implies\mathsf{\dfrac{3}{2k}=\dfrac{2}{5}}$

$\implies\mathsf{15=4k}$

$\implies\boxed{\bf\;k=\dfrac{15}{4}}$