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Question
If the system of equations

$$ \begin{aligned} & 2 x+3 y-z=5 \\\\ & x+\alpha y+3 z=-4 \\\\ & 3 x-y+\beta z=7 \end{aligned} $$

has infinitely many solutions, then $13 \alpha \beta$ is equal to :
1110
1120
1210
1220

Solution

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