Select the correct answer. Which statement about this system of equations is true? A diagonal curve rises through (negative 5, 4 point 1), (negative 3, 5), (0, 6), (3, 7) and (6, 8). A diagonal curve rises through (negative 6, 6), (negative 5, 3), (0,
To determine the correct answer about the system of equations represented by the two diagonal curves, we can analyze the key features of the curves:
- The first curve rises through the points given (negative 5, 4.1), (negative 3, 5), (0, 6), (3, 7), and (6, 8).
- The second curve rises through the points (negative 6, 6), (negative 5, 3), (0, 4), (3, -3), and (5, -2.1).
Let's examine:
1. **Intersection Points**: Identify if the two curves intersect anywhere. This will help us figure out the nature of the solutions. A unique solution occurs if they intersect at exactly one point.
2. **Specific Points**:
- The point (0, 6) is on the first curve but not on the second curve.
- The point (0, -4) is not mentioned in relation to either curve and hence cannot be a solution.
Since there are no overlapping points that the two curves meet, we can conclude the following:
- **If they do not intersect** at any point, then the system has no solution.
Based on this reasoning, the correct answer is:
**A. The system has no solution.**
Update (2025-10-29):
To determine which statement about the system of equations is true, we need to analyze the two curves described:
1. The first curve rises and passes through the points:
- (-5, 4.1)
- (-3, 5)
- (0, 6)
- (3, 7)
- (6, 8)
This suggests that this curve is continuously increasing in y as x increases.
2. The second curve rises and passes through the points:
- (-6, 6)
- (-5, 3)
- (0, 4)
- (3, -3)
- (5, -2.1)
This curve exhibits a downward trend at certain intervals (for example, it decreases as it moves from (-5, 3) to (0, 4) then drops significantly afterward).
Now, let's consider the potential solutions:
- The curves will intersect at points where they share the same x and y coordinates.
- The first curve crosses the point (0, 6) while the second curve crosses at (0, 4). Therefore, at x = 0, the y-values for the two curves are different: the first curve has y = 6 and the second curve has y = 4.
- There are no points indicated in the descriptions where the two curves share the same coordinates based on the points provided.
- Since they do not intersect at any point, there is no solution to this system of equations.
Therefore, the correct answer is:
A. The system has no solution.
Update (2025-10-29):
To determine the correct answer, we need to analyze the given information about the two curves.
1. The first curve rises through the points:
- (-5, 4.1)
- (-3, 5)
- (0, 6)
- (3, 7)
- (6, 8)
2. The second curve rises through the points:
- (-6, 6)
- (-5, 3)
- (0, 4)
- (3, -3)
- (5, -2.1)
To find the intersections of these two curves, or solutions to the system of equations, we can look at the specific points mentioned:
- For (0, 6), the first curve passes through this point. However, the second curve does not pass through (0, 6); instead, it passes through (0, 4). Thus, (0, 6) is not a solution for both curves.
- The point (0, -4) is not mentioned for either curve, so we cannot conclude it as a solution.
- There are no indications of any intersections between the curves at any other points based on the provided coordinates.
Since the two curves do not intersect at any common coordinate, the system of equations has no solutions.
Therefore, the correct answer is:
A. The system has no solution.