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OME 1973 Problem 2

    Determine all solutions of the system {2x−5y+11z−6=0−x+3y−16z+8=04x−5y−83z+38=03x+11y−z+9>0\begin{cases} 2x - 5y + 11z - 6 = 0 -x + 3y - 16z + 8 = 0 4x - 5y - 83z + 38 = 0 3x + 11y - z + 9 > 0 \end{cases}

    in which the first three are equations and the last one is a linear inequality.

    Dataset text AI-MO AoPS. Quoted with source.

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