To determine how many solutions the system of linear equations has based on the description provided, we need to consider the following:
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One line defined by two points: The line that passes through the points (0, -1) and (1, -3) represents one equation. A line in the coordinate plane represents a set of solutions.
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Another point: The point (-1, 0) is mentioned, and it is identified as a potential solution. However, since there's just one line given and a point, we need to examine if this point lies on the line.
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Intersection of solutions:
- If the point (-1, 0) lies on the line, then the system has exactly one solution at that point.
- If the point (-1, 0) does not lie on the line, then the line represents all solutions, and the system does not have a solution at (-1, 0).
- There's no mention of a second line for comparison, so we cannot have no solution or infinitely many solutions without more context.
To succinctly answer the question:
- If the graph indicates that (-1, 0) is on the line, there would be one solution.
- If not, then (-1, 0) is irrelevant, and we could only say that the line has infinitely many solutions along it.
From the options provided, since no specific second equation or line is present to indicate the possibility of "No solution" or "Infinitely many solutions,” and "One solution at (0, -1)" does not match the provided points that form the line, we conclude:
The answer aligned with the context would be: One solution at (−1, 0), assuming that point lies on the line.
If (-1, 0) does not, then you might want to confirm if there are infinitely many solutions along the line.