Question

Find the value of $k$, if the lines $3x+2ky=2$ and $2x+5y=-1$ has infinite solutions.

Answer 1

$3x+2ky-2=0$; $2x+5y+1=0$

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

For parallel lines

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

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

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

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