Question

The Value Of K For Which Kx+3y-k+3=0 And 12x+ky=k, Have Infinite Solution Is:


Option A :0

Option B :6

Option C: -6

Option D: 1

Answer 1

Heya !!

KX + 3Y - K + 3 = 0 --------(1)



12X + KY = K

12X + KY - K = 0 ------(2)


These equations are of the form of A1X+ B1Y + C1 = 0 and A2X + B2Y + C2 = 0


Where,


A1 = K , B1 = 3 and C2 = -K+3


And,

A2 = 12 , B2 = K and C2 = -K



For infinite solution we must have :


A1/A2 = B1/B2 = C1/C2



K/12 = 3/K = -K+3/-K



K/12 = 3/K = K-3/K



K/12 = 3/K and 3/K = K-3/K



K² = 36 and K²-6K = 0


K = ✓36 and K ( K -6 ) = 0



K = 6 or -6 and ( K = 0 or K = 6 )



K = 6


Hence,


The given equations has infinitely many solution when k = 6.

Answer 2

Answer:

6............................B