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Determine which of the graphs is the graph of a system of inequalities with no solutions.(1 point)

Responses

Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.

Image with alt text: Two dashed lines and four points are graphed on a coordinate plane. The x-axis ranges from negative 6 to 30 in increments of 2. The y-axis ranges from negative 5 to 15 in increments of 1.

Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A solid line with arrows at both ends is plotted, and various regions of the graph are marked.

1 answer

To determine which graph represents a system of inequalities with no solutions, we need to look for regions that are completely separated so that no point satisfies all inequalities simultaneously.

  1. The first graph: If there are two solid lines in a way that the shaded regions do not overlap at all, this could indicate a system with no solutions.

  2. The second graph: Dashed lines typically indicate inequalities, and the presence of four distinct points could imply regions that may overlap. This usually suggests that there might be solutions.

  3. The third graph: Similar to the first one, a solid line with various marked regions could represent overlaps or separations, but without seeing the precise arrangement, it's hard to determine definitively.

Based on your description, it sounds like the first graph is the most likely candidate for a system of inequalities with no solutions, especially if the shaded regions from the lines do not intersect or overlap at all. Ensure to confirm that the regions are indeed completely separate without any overlap.