To determine the correct statement about the graphed system of inequalities based on your description, we generally analyze the intersections of the dashed lines.
In a system of inequalities, the solution set can be represented in different ways:
- Infinite Solutions - This occurs when the lines are parallel or if one line overlaps with another (meaning they represent the same region).
- No Solutions - This occurs if the lines do not intersect and do not bound any overlapping region (for example, if one inequality is entirely above or below the other).
- One Solution - This occurs when the two lines intersect at a single point, which is often not the case for inequalities since they typically involve regions rather than points.
- Two Solutions - This generally applies if the inequalities are set in a way that creates two feasible regions of overlap at distinct points.
Based on the possibilities:
- If the lines intersect in a way that creates shaded regions that overlap, indicating more than one feasible area, then the statement "The system has infinite solutions" would be true.
- If the lines create distinct regions with no overlap, then "The system has no solutions" would be accurate.
Without a visual or more specifics about the lines:
- If the lines create regions where all points can satisfy the inequalities, "The system has infinite solutions" is the possible correct statement.
- Conversely, if they entirely separate the plane into regions with no valid overlaps, then "The system has no solutions."
In conclusion, the assessment would depend significantly on the visual representation, but generally speaking, if you observe overlapping shaded regions, you would select "The system has infinite solutions." If you notice that the lines separate into distinct regions without overlap, then "The system has no solutions." Please check the graph to confirm.
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