Question

 If the lines given by

3x + 2ky = 2

2x + 5y + 1 = 0

are parallel, then the value of k is

(A) 5/4                                                            

(B) 2/5

(C) 15/4                                                          

(D) 3/2

​

Answer 1

Answer: (C) 15/4

Explanation:

For parallel lines

a1/a2=b1/b2≠c1/c2

=> 3/2=2k/5

=> k=15/4

hope it's helps you ❤️

Answer 2

$\huge\boxed{\underline{\underline{\green{Solution}}}} </p><p>$

$\displaystyle \: \longmapsto \: \:$FORMULA TO BE IMPLEMENTED :

A pair of Straight Lines

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

Is said to be parallel if

$\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}$

$\displaystyle \: \longmapsto \: \:$CALCULATION :

Given pair of linear equations

$3x +2ky - 2 =0 \: \: and \: \: 2x + 5y +1=0$

Comparing with

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

We get

$\displaystyle \: a_1 = 3 \: , \: b_1 = 2k</p><p> \: , c_1= - 2\: and \: \: a_2 = 2 \: , \: b_2 = 5\: , \: \: c_2= 1$

Now $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}$

gives

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

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

RESULT

If the lines given by

3x + 2ky = 2

2x + 5y + 1 = 0

are parallel, then the value of k is

(C) 15/4