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 infinite solutions.
The system has infinite solutions.
The system has no solutions.
The system has no solutions.
The system has one solution.
The system has one solution.
Skip to navigation
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 infinite solutions.
The system has infinite solutions.
The system has no solutions.
The system has no solutions.
The system has one solution.
The system has one solution.
Skip to navigation
Answers
GPT-4o mini
To determine the correct statement regarding the system of inequalities based on your description of the Cartesian coordinate plane and the dashed lines with arrows plotted on it, we can analyze the possible relationships:
1. **Two parallel lines**: If the two dashed lines are parallel, they will not intersect at all, which means there would be no solution to the system of inequalities.
2. **Intersecting lines**: If the lines intersect, they divide the plane into several regions. The feasible solution region created by the inequalities can potentially be infinite, depending on how the inequalities are structured.
3. **Same line or coincident lines**: If the lines are actually the same (coincident), then every point along that line would be a solution, which would also mean infinite solutions.
Given that the lines are dashed (indicating that they are not included in the solution set), the presence of parallel lines typically leads to a conclusion of "no solutions" because the inequalities would either be contradictory or not overlap at any points.
Therefore, without the exact configuration of the lines or inequalities used, a reasonable conclusion would be:
- If the lines do not intersect (are parallel), then the correct statement would be "The system has no solutions."
If you can provide more information about the lines and their respective inequalities, a more specific answer can be given. However, based on the information given, the safest assumption is indeed "The system has no solutions."
1. **Two parallel lines**: If the two dashed lines are parallel, they will not intersect at all, which means there would be no solution to the system of inequalities.
2. **Intersecting lines**: If the lines intersect, they divide the plane into several regions. The feasible solution region created by the inequalities can potentially be infinite, depending on how the inequalities are structured.
3. **Same line or coincident lines**: If the lines are actually the same (coincident), then every point along that line would be a solution, which would also mean infinite solutions.
Given that the lines are dashed (indicating that they are not included in the solution set), the presence of parallel lines typically leads to a conclusion of "no solutions" because the inequalities would either be contradictory or not overlap at any points.
Therefore, without the exact configuration of the lines or inequalities used, a reasonable conclusion would be:
- If the lines do not intersect (are parallel), then the correct statement would be "The system has no solutions."
If you can provide more information about the lines and their respective inequalities, a more specific answer can be given. However, based on the information given, the safest assumption is indeed "The system has no solutions."