To determine which graph corresponds to a system of inequalities with no solutions, we need to look for cases where the shaded regions created by the inequalities do not overlap at all. This typically happens when the constraints set by the inequalities are contradictory and cannot satisfy any common area.
Here’s how to analyze the options:
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Single solid line: If there's only one line, it can represent an inequality, but it won’t lead to a system with no solutions unless there’s another line or constraint contradicting it.
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Two solid lines: If both lines are solid and the shaded regions do not overlap, it could indicate no solution. If they are parallel but shaded on opposite sides, they conflict.
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Dashed lines with regions: Dashed lines usually represent inequalities and can create regions of solutions. If both lines create opposing regions, the system could have no solution.
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Another set of two solid lines: Similar to the previous case with two solid lines, we need to check if their regions conflict.
From this reasoning, if we find a case where two lines either do not intersect or create opposite shaded regions with solid lines, we can conclude that there is no solution.
Without visual access to the graphs, I recommend focusing on the option with two solid lines that have shaded regions on opposite sides or conflicting shaded areas. That’s the graph that likely represents a system of inequalities with no possible solutions.