Question

find the value of k for which the given lines 3x+2ky=2 and 2x+5y+1=0 are parallel.​

Answer 1

$\huge{\boxed{\mathfrak{Answer}}}$

Linear Equations have two types :

i) Consistent and ii) Inconsistent

i) Consistent includes :

• Intersecting lines

a₁ / a₂ ≠ b₁ / b₂

UNIQUE SOLUTION

• Coincident lines

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

INFINITE SOLUTIONS

i) Inconsistent includes :

• Parallel lines

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂

NO SOLUTION

Now answer of your question starts from here :

√ To find the Value of "k".

√ Given lines are parallel.

√ 3x+2ky=2 and 2x+5y+1=0

• 3x + 2ky - 2  =  0

       2x + 5y + 1    =  0

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

• Parallel lines

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂   ( putting values )

• 3/2 = 2k/5
• 4k = 15
• k = 15/4

$\implies\boxed{\mathsf{Hence,\:the\:value\:of\:'k'\:=\:15/4}}$