Verified Solution • 2025–26 Session moderate

QJEEM21Ma853b: JEE Main 2021 Mathematics - Class 12 JEEM21Ma853b Solution: If the system of equations kx + y + 2z = 1 3x y 2z = 2 2x 2y 4z …

If the system of equations

kx + y + 2z = 1

3x −- y −- 2z = 2

−- 2x −- 2y −- 4z = 3

has infinitely many solutions, then k is equal to __________.

Step-by-Step Verified Solution

D = 0

⇒|k123−1−2−2−2−4|=0

⇒\Rightarrow k (4 −- 4) −- 1 ( −- 12 −- 4) + 2 ( −- 6 −- 2)

⇒\Rightarrow 16 −- 16 = 0

Also, D1=D2=D3=0{D_1} = {D_2} = {D_3} = 0

⇒D2=|k1232−2−23−4|=0

⇒\Rightarrow k( −- 8 + 6) −- 1( −- 12 −- 4) + 2(9 + 4) = 0

⇒\Rightarrow −- 2k + 16 + 26 = 0

⇒\Rightarrow 2k = 42

⇒\Rightarrow k = 21

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