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.

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.
Skip to navigation

Answer 1

To determine which graph represents a system of inequalities with no solutions, we need to look for the configuration of lines and shading.

A system of inequalities has no solutions when the regions defined by the inequalities do not overlap at all. This usually occurs when:

• There are two parallel lines with respective shading on opposite sides of each line. This means the shaded regions do not intersect anywhere.

Let's summarize the options based on your descriptions:

1. One solid line and various shaded regions.
2. Two solid lines with various shaded regions.
3. Two solid lines with various shaded regions (same as option 2).
4. Two dashed lines with points plotted, but no shading described, which may indicate intersections.

Since we are looking for a clear indication of no overlap, options 2 and 3 (the ones with two solid lines) would typically represent parallel inequalities with non-overlapping regions if the shaded areas are on opposite sides of each line. We cannot definitively identify which of those options has no solution without seeing the shading.

If the graphical elements corresponding to any of the options clearly show two parallel lines with opposite shadings or distinctly non-overlapping shaded areas, that would indicate a system with no solutions.

Without visual context, I recommend you look for:

• 2 solid lines that are parallel (and if their shading is on opposite sides, they represent a system with no solutions).

In summary, choose the graph with two solid lines that indicate no overlapping shaded regions for no solutions.