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.

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.

Answer 1

To determine which of the graphs represents a system of inequalities with no solutions, we need to look for a case where the shaded regions (indicating the solutions to each inequality) do not overlap at any point.

1. Graph with 2 solid lines:

   • If the solid lines are parallel and there is no region where the inequalities overlap, this system would have no solutions.

2. Graph with 1 solid line:

   • A single line would indicate only one inequality; hence, there can still be solutions depending on how it's shaded.

3. Graph with 2 solid lines:

   • Similar to the first option, if these lines intersect and create regions with non-overlapping shaded areas, then this also would indicate no solutions.

In summary, the graph with two solid lines that are parallel (or any similar configuration creating non-overlapping regions) is the graph representing a system of inequalities with no solutions.

If only one specific option displays solid lines without an intersection or overlapping shaded regions, that will be your answer. Note that without the visuals, I can't specify exactly which one it is, but follow the analysis above to identify it among your options.