If the lines given by 3x+ 2ky = 2
Question:

If the lines given by 3x+ 2ky = 2 and 2x + 5y = 1 are parallel, then the value of 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), $\frac{3}{2}=\frac{2 k}{5}$

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

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