Ask a New Question
Menu

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

1 answer

To determine which graph represents a system of inequalities with no solutions, we need to identify a scenario where the shaded regions do not overlap at all. This usually occurs when the constraints defined by the inequalities contradict each other.

  1. Single line with shaded region - This would likely define a half-plane. It can have solutions unless there’s another line contradicting it.

  2. Two solid lines with regions - If the two lines are parallel and shaded in opposite directions, there would be no overlapping region, indicating no solutions.

  3. Two dashed lines - Dash lines typically represent inequalities that do not include the line itself. If they divide the plane into sections without overlap, there could also be no solutions.

  4. Another set of two solid lines - Similar to option 2, if they are parallel with opposite shading, there could be no intersection.

To conclude, the correct option showing a system of inequalities with no solutions will likely be the scenario with two parallel lines (solid) shading in opposite directions or two dashed lines dividing the plane without any shared region.

Without the actual visual, I suggest looking for the graph where:

  • The shaded regions are completely separate and do not overlap at all.
  • The lines are either solid and parallel with the shaded areas going in opposite directions or dashed with no points of intersection.

If you can specify more details about the shading of those lines, I can provide a more focused answer!