Substitute \((x, y) = (2, 13)\) into the given linear inequality \(0x + y \mathrel{\#<} 0\).
This gives us \(0 \cdot 2 + 1 \cdot 13 = 13\).
Since \(13 \mathrel{\#<} 0\) is false, the ordered pair \((2, 13)\) is not a solution to the inequality.
Substitute \((x, y) = (-7, -37)\) into the given linear inequality \(0x + y \mathrel{\#<} 0\).
This gives us \(0 \cdot -7 + 1 \cdot -37 = -37\).
Since \(-37 \mathrel{\#<} 0\) is true, the ordered pair \((-7, -37)\) is a solution to the inequality.
Substitute \((x, y) = (-9, -39)\) into the given linear inequality \(0x + y \mathrel{\#<} 0\).
This gives us \(0 \cdot -9 + 1 \cdot -39 = -39\).
Since \(-39 \mathrel{\#<} 0\) is true, the ordered pair \((-9, -39)\) is a solution to the inequality.