If the lines given by $ 3 x+2 k y=2 $ and $ 2 x+5 y+1=0 $ are parallel, then the value of $ k $ is
(A) $ \frac{-5}{4} $
(B) $ \frac{2}{5} $
(C) $ \frac{15}{4} $
,b>(D) $ \frac{3}{2} $

Given:

The lines given by \( 3 x+2 k y=2 \) and \( 2 x+5 y+1=0 \) are parallel.

To do:

We have to find the value of \( k \).

Solution:

We know that,

The condition for parallel lines is,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$

\( 3 x+2 k y=2 \) and \( 2 x+5 y+1=0 \) are parallel.

Here,

$a_1=3, b_1=2k, c_1=-2$

$a_2=2, b_2=5, c_2=1$

Therefore,

$\frac{3}{2}=\frac{2k}{5}≠\frac{-2}{1}$

$\frac{3}{2}=\frac{2k}{5}$

$2(2k)=5(3)$

$4k=15$

$k=\frac{15}{4}$

The value of $k$ is $\frac{15}{4}$. 

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Updated on: 10-Oct-2022

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