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. A solid line with arrows at both ends is 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. A solid line with arrows at both ends is 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. 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.

Answer 1

To determine which graph represents a system of inequalities with no solutions, we need to look for scenarios where the shaded regions for the inequalities do not overlap at all. This would indicate that there is no possible solution that satisfies all inequalities simultaneously.

1. The first graph with one solid line may indicate a single inequality, which could potentially have solutions.
2. The second graph with two solid lines has the potential for overlapping regions; thus, it could have solutions.
3. The third graph with two dashed lines could represent inequalities as well. Depending on their placement, they could either have overlapping solutions or none at all.
4. The fourth graph with two solid lines also could have overlapping regions.

To conclude, you would want to see a case where the regions shaded for the inequalities are completely separated, meaning they do not share any common area.

Without visuals or further details, it's hard to definitively name the correct response. However, typically, the graph with two parallel lines (if they don't intersect or share any shaded area) is a common configuration that results in no solutions.

To summarize, look for the graph where two inequalities create regions that do not intersect or share any area. If you can identify that graph, that would be the one with no solutions.