Question

If the lines 3x+2ky=2 and 2x+5y+1=0 r parallel , then find the value of k.

Answer 1

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

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

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

$\textsf{The value of k}$

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

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

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

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

$\implies\mathsf{m_1=m_2}$

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

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

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

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

Answer 2

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