Question

Use the image to answer the question.

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 dashed lines with arrows at both ends are plotted, and various regions of the graph are marked.

Select a true statement to describe the graphed system of inequalities.

(1 point)
Responses

The system has two solutions.
The system has two solutions.

The system has one solution.
The system has one solution.

The system has infinite solutions.
The system has infinite solutions.

The system has no solutions

Answer 1

I can't see the graph you mean — could you upload the image or describe the two lines and which side of each line is shaded (for example: "line y = x is dashed, shading above; line y = -x+1 is dashed, shading below")?

If you prefer to decide yourself, here’s how to tell which answer is correct:

- Dashed lines mean strict inequalities (< or >), so points on the line are NOT included.
- If the shaded regions overlap in a two-dimensional region (an area), there are infinite solutions.
- If the shaded regions do not overlap at all, there are no solutions.
- If the shaded regions meet exactly at a single point, there is one solution — but if that point lies on a dashed line for either inequality it is not included, so then there would actually be no solutions.
- Two solutions is extremely unlikely for linear inequalities (would require intersection to be exactly two isolated points), so that choice is almost never correct for standard linear systems.

Send the picture or the line equations and shading directions and I’ll pick the correct option.