If the system of equations x + y + z = 6, 2x + 5y + z = , x + 2y + 3z = 14 has infinitely many solutions, then + is equal to

JEE Main 2022 Mathematics question

If the system of equations x + y + z = 6, , x + 2y + 3z = 14 has infinitely many solutions, then is equal to

Answer: (3)

From x + y + z = 6 and x + 2y + 3z = 14 we get y + 2z = 8, so y = 8 − 2z and x = z − 2. Substituting in : $2(z - 2) + 5(8 - 2z) + α z =

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Question ID VK-035048