Question
Use the system of inequalities graphed below to answer the questions. What is the inequality symbol of the green line? What is the inequality symbol of the purple line? Is the point (-3, -5) a solution to the system of inequalities? Is the point (1, 6) a solution to the system of inequalities?
Answers
GPT-4o mini
To determine the inequality symbols of the lines based on the graph, you typically look at the shading on either side of the lines and whether the lines themselves are solid or dashed:
1. **Green Line**: If the area above (or below) this line is shaded, then it generally indicates a 'greater than' (>) or 'less than' (<) inequality. If the line is solid, the inequality includes equality (≥ or ≤). If the line is dashed, it does not include equality (> or <).
2. **Purple Line**: Similar logic applies. The shading will indicate whether it is a 'greater than' or 'less than' and whether it is solid or dashed will dictate if equality is included.
For the specific points:
- **Point (-3, -5)**: To determine if this point is a solution, substitute its coordinates into the inequalities represented by the lines. If it satisfies all inequalities, it is a solution.
- **Point (1, 6)**: Perform the same check as above. Substitute this point into the inequalities to see if it satisfies all of them.
Without the graph or the equations of the lines, I can't provide the specific inequality symbols or confirm the solutions for the points. However, if you describe the graph or provide the equations of the lines, I can help you analyze the inequalities and check the points!
1. **Green Line**: If the area above (or below) this line is shaded, then it generally indicates a 'greater than' (>) or 'less than' (<) inequality. If the line is solid, the inequality includes equality (≥ or ≤). If the line is dashed, it does not include equality (> or <).
2. **Purple Line**: Similar logic applies. The shading will indicate whether it is a 'greater than' or 'less than' and whether it is solid or dashed will dictate if equality is included.
For the specific points:
- **Point (-3, -5)**: To determine if this point is a solution, substitute its coordinates into the inequalities represented by the lines. If it satisfies all inequalities, it is a solution.
- **Point (1, 6)**: Perform the same check as above. Substitute this point into the inequalities to see if it satisfies all of them.
Without the graph or the equations of the lines, I can't provide the specific inequality symbols or confirm the solutions for the points. However, if you describe the graph or provide the equations of the lines, I can help you analyze the inequalities and check the points!