To determine which description is true about the graphed system of inequalities, you need to consider the nature of the lines and the regions they create.
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Solid Line: A solid line typically represents an inequality that includes equal to (e.g., \( \leq \) or \( \geq \)). This means that points on this line are part of the solution set.
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Dashed Line: A dashed line represents an inequality that does not include equal to (e.g., \( < \) or \( > \)). This means that points on this line are not part of the solution set.
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Shaded Regions: The areas that are shaded indicate where the solutions to the inequalities are located. If the shaded regions overlap, there are points that satisfy both inequalities, resulting in infinite solutions.
Based on typical scenarios you might see in a Cartesian coordinate plane:
- If the two lines do not intersect and represent contradictory inequalities, there could be no solutions.
- If the lines intersect, check the shaded regions. If they overlap, there would be infinite solutions in the overlapping area.
Given these points, if the system's inequalities show overlapping shaded regions, the correct choice would generally be:
The system has infinite solutions.
If the lines do not intersect and fit contradictory conditions, it could be:
The system has no solutions.
Without the specific image, it's not possible to give a definitive answer. However, you can use this reasoning to analyze your particular case.
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