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 no solutions.
The system has no solutions.
The system has two solutions.
The system has two solutions.
The system has infinite solutions.
The system has infinite solutions.
The system has one solution.
Select a true statement to describe the graphed system of inequalities.
(1 point)
Responses
The system has no solutions.
The system has no solutions.
The system has two solutions.
The system has two solutions.
The system has infinite solutions.
The system has infinite solutions.
The system has one solution.
Answers
GPT-4o mini
Without seeing the graph, I cannot provide a visual interpretation of the inequalities or regions. However, I can explain the possible scenarios regarding systems of inequalities:
1. **The system has no solutions.** - This occurs when the regions defined by the inequalities do not overlap at all.
2. **The system has two solutions.** - This is less common; generally, systems of inequalities interact in such a way that they allow for either one solution, none, or infinitely many solutions.
3. **The system has infinite solutions.** - This is true when there is a region of overlap where an infinite number of points satisfy all inequalities.
4. **The system has one solution.** - This is possible if the overlap point is discrete and represents a single point.
If the lines defined by the inequalities create overlapping areas, the likely outcome is infinite solutions. If they are parallel and do not intersect, or if they form a unique overlap at a point, then the options of no solutions or one solution would apply.
To select the correct statement, you need to assess whether the regions of overlap suggest infinite possibilities (infinite solutions) or limited outcomes (one solution or none) based on the graphical representation.
If you provide more specific details about the positions of the dashed lines and the shaded regions, I can assist you in determining the correct response with greater certainty.
1. **The system has no solutions.** - This occurs when the regions defined by the inequalities do not overlap at all.
2. **The system has two solutions.** - This is less common; generally, systems of inequalities interact in such a way that they allow for either one solution, none, or infinitely many solutions.
3. **The system has infinite solutions.** - This is true when there is a region of overlap where an infinite number of points satisfy all inequalities.
4. **The system has one solution.** - This is possible if the overlap point is discrete and represents a single point.
If the lines defined by the inequalities create overlapping areas, the likely outcome is infinite solutions. If they are parallel and do not intersect, or if they form a unique overlap at a point, then the options of no solutions or one solution would apply.
To select the correct statement, you need to assess whether the regions of overlap suggest infinite possibilities (infinite solutions) or limited outcomes (one solution or none) based on the graphical representation.
If you provide more specific details about the positions of the dashed lines and the shaded regions, I can assist you in determining the correct response with greater certainty.