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

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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.
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.
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Answer 1

To determine which graph corresponds to a system of inequalities with no solutions, we need to look for cases where the shaded regions created by the inequalities do not overlap at all. This typically happens when the constraints set by the inequalities are contradictory and cannot satisfy any common area.

Here’s how to analyze the options:

1. Single solid line: If there's only one line, it can represent an inequality, but it won’t lead to a system with no solutions unless there’s another line or constraint contradicting it.

2. Two solid lines: If both lines are solid and the shaded regions do not overlap, it could indicate no solution. If they are parallel but shaded on opposite sides, they conflict.

3. Dashed lines with regions: Dashed lines usually represent inequalities and can create regions of solutions. If both lines create opposing regions, the system could have no solution.

4. Another set of two solid lines: Similar to the previous case with two solid lines, we need to check if their regions conflict.

From this reasoning, if we find a case where two lines either do not intersect or create opposite shaded regions with solid lines, we can conclude that there is no solution.

Without visual access to the graphs, I recommend focusing on the option with two solid lines that have shaded regions on opposite sides or conflicting shaded areas. That’s the graph that likely represents a system of inequalities with no possible solutions.

Answer 2

which option

Answer 3

Based on the descriptions you've provided, the best option that is likely to represent a system of inequalities with no solutions would be the one with two solid lines that create non-overlapping shaded regions.

However, since I cannot visually see the graphs, I recommend selecting the response that mentions two solid lines with arrows if they indicate opposite shaded regions. This configuration would imply that there are constraints in place that cannot be satisfied simultaneously, leading to no solutions.

If you could specify any details on the shading or positions of the lines in either option, I could confirm further. But based on your descriptions alone, the option with two solid lines showing opposing shaded regions is the most likely candidate for a system with no solutions.

Answer 4

1 2 3 or 4

Answer 5

Since I don’t have access to the visuals of the graphs, I will rely on your descriptions. Generally, a system of inequalities with no solutions will have constraints that create non-overlapping regions.

Based on the standard characteristics of the options you provided:

• If any of the options describe two solid lines with their shaded regions on opposite sides, then that would likely be option 2 or option 4.
• If you specified that option 2 describes two solid lines intersecting in such a way that they create conflicting shaded regions, that would most likely indicate no solutions.

Therefore, I recommend choosing either option 2 or option 4, depending on which of these two displays the situation described.

If there's further description of each option's criteria, that would help pinpoint the exact choice!