Question
Multiple Choice Question
The graph below represents a system of equations.
A line passing through (-2, 0) and (0, -3), another line passing through (0, 1) and (2, 0) intersect at (-4, 3).
Which of the following statements is true?
A.
The system has infinite solutions.
B.
The solutions to the system are
and
.
C.
The solution to the system is
.
D.
The system has no solution.
Answers
GPT-4o mini
To analyze the scenario based on the description provided about the lines in the graph, let’s break down the statements:
1. **Identifying the lines and intersection**:
- The first line passes through points (-2, 0) and (0, -3).
- The second line passes through points (0, 1) and (2, 0).
Given the description, the lines intersect at a single point (-4, 3).
2. **Evaluating the statements**:
- **A. The system has infinite solutions.**
- This is false, as the lines intersect at a single point.
- **B. The solutions to the system are and.**
- This statement is incomplete and hence does not provide complete information.
- **C. The solution to the system is .**
- This statement is also incomplete without specifying what the solution is (likely meant to say (-4, 3), based on the intersection point).
- **D. The system has no solution.**
- This is false, as the lines do intersect.
Given that the lines intersect at a single point (-4, 3), the most accurate option, even though it's incomplete, would point to **C** as the correct choice for stating the solution if it were complete.
Assuming it were to say "The solution to the system is (-4, 3)", that would be true based on the description. Since the other options (A and D) are false and B is incomplete, **C** stands as the most relevant answer here, although it should ideally state the actual solution.
For a final selection:
**C** (assuming it completes to point to the solution).
1. **Identifying the lines and intersection**:
- The first line passes through points (-2, 0) and (0, -3).
- The second line passes through points (0, 1) and (2, 0).
Given the description, the lines intersect at a single point (-4, 3).
2. **Evaluating the statements**:
- **A. The system has infinite solutions.**
- This is false, as the lines intersect at a single point.
- **B. The solutions to the system are and.**
- This statement is incomplete and hence does not provide complete information.
- **C. The solution to the system is .**
- This statement is also incomplete without specifying what the solution is (likely meant to say (-4, 3), based on the intersection point).
- **D. The system has no solution.**
- This is false, as the lines do intersect.
Given that the lines intersect at a single point (-4, 3), the most accurate option, even though it's incomplete, would point to **C** as the correct choice for stating the solution if it were complete.
Assuming it were to say "The solution to the system is (-4, 3)", that would be true based on the description. Since the other options (A and D) are false and B is incomplete, **C** stands as the most relevant answer here, although it should ideally state the actual solution.
For a final selection:
**C** (assuming it completes to point to the solution).