Question

Question No. 4
If the lines given by 3x+2ky=6 and 2x+5y-4=0 are parallel then the value of k is
-5/4
A)
15/4
B)
2/5
C)
None of these
D)​

Answer 1

Answer:

B) 15/ 4

Step by step explaination:

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then what is the value of k?

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14 Answers



Mohil Khare, Writer at wikiHow (2014-present)

Answered July 12, 2017

For the lines to be parallel, the slopes of the lines MUST be equal.

Lines:

3x + 2ky - 2 = 0 … (1)

2x + 5y + 1 = 0 … (2)

Now, convert 1 and 2 into y = mx + c form where m is the slope.

for 1,

y = (-3/2k)x + (1/k)

for 2,

y = (-2/5)x - (1/5)

So now for both lines to be parallel, (-3/2k) must be equal to (-2/5)

Answer 2

Answer:

$\bigstar{\bold{Option\:B:\dfrac{15}{4} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

Lines are parallel and the equation are:

• 3x + 2ky = 6
• 2x + 5y -4 = 0

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The value of k

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ The given lines are

  3x + 2ky - 6 =0

  2x + 5y - 4 = 0

→ Since it is given that the lines are parelle, there are no solutions for this equations and it is inconsistent.

→ That is,

  $\dfrac{a_1}{a_2} =\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$

where a₁ = 3, a₂ = 2, b₁ = 2k, b₂ = 5, c₁ = -6, c₂ = -4

→ Substituting the value we get,

  $\dfrac{3}{2} =\dfrac{2k}{5} \neq \dfrac{-6}{-4}$

→ Taking the first part of equation,

   $\dfrac{3}{2} =\dfrac{2k}{5}$

→ Cross multiplying,

   3 × 5 = 2k × 2

   15 = 4k

   k = 15/4

→ Hence the value of k is 15/4

$\boxed{\bold{k=\dfrac{15}{4} }}$

→ Hence option B is correct

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ If a pair of equations have unique solution, the lines will be intersecting and consistent.

  $\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}$

→ If a pair of equations have infinite solutions, the lines will be coincident and will be consistent.

 $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2} =\dfrac{c_1}{c_2}$

→ If a pair of equations have no solution, the lies will be parallel and inconsistent.

  $\dfrac{a_1}{a_2} =\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$