Verified Solution • 2025–26 Session moderate

QJEEM19Ma089e: JEE Main 2019 Mathematics - Class 12 JEEM19Ma089e Solution: If the system of linear equations x 4y + 7z = g…

If the system of linear equations
x −- 4y + 7z = g
       3y −- 5z = h
−- 2x + 5y −- 9z = k
is consistent, then :

Multiple Choice Options

  • A g + 2h + k = 0
  • B g + h + 2k = 0
  • C 2g + h + k = 0
  • D g + h + k = 0

Step-by-Step Verified Solution

x −- 4y+7z=g4y + 7z = g
       3y3y −- 5z=h5z = h
−- 2x+5y2x + 5y −- 9z=k9z = k

D=|1−4703−5−25−9|

D=1(−27+25)−2(20−21)D = 1\left( { - 27 + 25} \right) - 2\left( {20 - 21} \right)

D=−2+2=0D = - 2 + 2 = 0

If system is consistent then D1=D2=D3=0{D_1} = {D_2} = {D_3} = 0

|1−4g03h−25k|=0

1(3k−5h)−2(−4h−3g)=01\left( {3k - 5h} \right) - 2\left( { - 4h - 3g} \right) = 0

3k−5h+8h+6g=03k - 5h + 8h + 6g = 0

6g+3h+3k=06g + 3h + 3k = 0

2g+h+k=02g + h + k = 0

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