If the system of linear equations x-2 y+z=-4 2 x+\alpha y+3 z=5 3 x-y+\beta z=3 has infinitely many solutions, then 12 \alpha+13 \beta is equal to [31-Jan-2024 Shift 1]

JEE Main 31-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 8 of 90

Marks: +1, -0

If the system of linear equations
x−2y+z=−4
2x+αy+3z=5
3x−y+βz=3
has infinitely many solutions, then 12α+13β is equal to

[31-Jan-2024 Shift 1]

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