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

Question

Responses

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: 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.

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: 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.

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: 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.

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.

Answer 1

To determine which graph represents a system of inequalities with no solutions, we need to look for a scenario where the shaded regions or feasible areas do not overlap at all. This usually occurs when the lines representing the inequalities are parallel and do not intersect, or when the lines intersect but the regions they define do not overlap.

From your description, the following can be inferred:

1. First graph: Two solid lines that are plotted, which means both inequalities are inclusive. The presence of shaded regions could indicate overlapping solutions, but we need to see the actual lines and their respective shaded regions to be certain.

2. Second graph: Two dashed lines suggest that these inequalities are strict (not inclusive). This doesn't necessarily indicate no solution but could mean that if the lines are parallel and offset, the regions could also not overlap.

3. Third graph: This describes a similar situation to the first graph. Again, without the actual view of the shaded areas, it's hard to conclude.

4. Fourth graph: This one indicates a single solid line along with shaded regions. If this line creates an area where the shade does not allow for any overlapping regions with other inequalities (especially if there are none present), then this may indicate a lack of solutions.

Given the absence of specific details on the lines' positions and the shaded areas for all graphs, based on your description alone, it is likely that the second graph (with two dashed lines) could potentially represent a situation where the regions defined by the inequalities do not overlap if the lines are parallel and do not intersect.

However, the precise answer would ideally depend on knowing the relationships and positions of each of these lines and the specific regions they shade on the graph.