Question

If a pair of linear equations 3x + 2Ky = 2 and 2x + 5y + 1 = 0 are parallel to
each other, then the value of 'K'
A. 15\4
B. 3/2
C.5
C.4/15
​

Answer 1

Given :- If a pair of linear equations 3x + 2Ky = 2 and 2x + 5y + 1 = 0 are parallel to each other, then the value of 'K'

A. 15/4

B. 3/2

C.5

C.4/15

Solution :-

we know that,

• A linear equation in two variables represents a straight line in 2D Cartesian plane .

• If we consider two linear equations in two variables, say :-

➻ a1x + b1y + c1 = 0

➻ a2x + b2y + c2 = 0

Then :-

✪ Both the straight lines will be parallel if :-

a1/a2 = b1/b2 ≠ c1/c2.

➻ In this case , the system will have no solution.

➻ If a system has no solution, it is said to be inconsistent.

so, comparing a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 with given linear equations 3x + 2Ky - 2 = 0 and 2x + 5y + 1 = 0 we get,

• a1 = 3
• b1 = 2k
• c1 = (-2)
• a2 = 2
• b2 = 5
• c2 = 1

then,

→ a1/a2 = b1/b2 ≠ c1/c2

→ 3/2 = 2k/5 ≠ (-2/2)

→ 3/2 = 2k/5

→ 3 * 5 = 2 * 2k

→ 15 = 4k

→ k = (15/4) (Ans.)

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Answer 2

$\underline{\textbf{Given:}}$

$\textsf{The lines}$

$\mathsf{3x+2ky-2=0\;\;\&\;\;2x+5y+1=0\;are\;parallel}$

$\underline{\textbf{To find:}}$

$\textsf{The value of k}$

$\underline{\textbf{Solution:}}$

$\mathsf{Slope\;of\;3x+2ky-2=0\;is\;m_1=\dfrac{-3}{2k}}$

$\mathsf{Slope\;of\;2x+5y+1=0\;is\;m_2=\dfrac{-2}{5}}$

$\mathsf{Since\;the\;lines\;are\;parallel\;to\;each\;other,}$

$\mathsf{the\;slopes\;are\;equal}$

$\implies\mathsf{m_1=m_2}$

$\implies\mathsf{\dfrac{-3}{2k}=\dfrac{-2}{5}}$

$\implies\mathsf{-15=-4k}$

$\implies\mathsf{15=4k}$

$\implies\boxed{\mathsf{k=\dfrac{15}{4}}}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(A)\;is\;correct}$

$\underline{\textbf{Find more:}}$

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