Question

find the value of k for which the pair of equations 2x + K Y + 3 equal to zero 4 x + 6 Y - 5 equal to zero represent parallel lines

Answer 1

$\tt{Answer: k = 3}$

Step by step explanation:

Comparing the given equations : 2x + ky + 3 = 0 and 4x + 6y - 5 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

We get ,

a1 = 2 , b1 = k , c1 = 3;

a2 = 4 , b2 = 6 , c2 = -5;

Since , the lines are parallel,

a1/a2 = b1/b2 ≠ c1/c2

a1/a2 = b1/b2

2 / 4 = k / 6

( 2 × 6 )/4 = k

3 = k

Therefore ,

k = 3

Answer 2

$\huge{\mathfrak{\underline{\pink{AnSwEr:-}}}}$

k = 3

$\huge{\mathfrak{\underline{\blue{Explanation:-}}}}$

Equations are :-

1. 2x + ky + 3 = 0
2. 4x + 6y - 5 = 0

________________

In which

a1 = 2

b1 = k

c1 = 3

_________

And

a2 = 4

b2 = 6

c2 = -5

$\rule{200}{1}$

We know that :-

For parralel lines we have formula :-

${\underline{\boxed { \bf{\huge \frac{a_{1} }{a_{2} } \: = \: \frac{b_{1} }{b_{2} } \: \neq \: \frac{c _{1}}{c_{2} }}}}}$

______________[Put Values]

⇒ 2/4 = k/6

⇒ 2 × 6 = 4 × k

⇒ 12 = 4k

⇒ k = 12/4

⇒ k = 3

$\large{\bf{\star{\boxed{\boxed{\red{k \; = \; 3}}}}}}$