Question:
If the lines given by 3x+ 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is
(a) $-\frac{5}{4}$
(b) $\frac{2}{5}$
(c) $\frac{15}{4}$
(d) $\frac{3}{2}$
Solution:
(c) Condition for parallel lines is
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Given lines, $3 x+2 k y-2=0$
and $2 x+5 y-1=0$
Here, $a_{1}=3, b_{1}=2 k, c_{1}=-2$
and $a_{2}=2, b_{2}=5, c_{2}=-1$
From Eq. (i), $\frac{3}{2}=\frac{2 k}{5}$
$\therefore$ $k=\frac{15}{4}$