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4x4 system of 3 equalities and 1 inequality

Source: Spanish Mathematical Olympiad 1973 P2

December 22, 2022
inequalitiessystem of equationsSystemalgebra

Problem Statement

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.
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