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

Given: Two lines given by $3x+2ky=2$ and $2x+5y+1=0$ are parallel.

To do: To find the value of $k$.

Solution:

Here $a_1=3,\ b_1=2k,\ c_1=2$ and $a_2=2,\ b_2=5,\ c_2=-1$

For parallel lines,

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

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

$\Rightarrow 2\times2k=5\times3$

$\Rightarrow 4k=15$

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

Thus, for $k=\frac{15}{4}$, the given lines are parallel.

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Updated on: 10-Oct-2022

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