Classify the following graphs according to whether they have no solutions, one solution, or infinitely many solutions.
Understand the Problem
The question is asking to categorize the three provided graphs based on how many solutions they represent (no solutions, one solution, or infinitely many solutions) in a linear system context.
Answer
- **No Solutions**: Graph 1 - **One Solution**: Graph 2 - **Infinitely Many Solutions**: Graph 3
Answer for screen readers
- No Solutions: Graph 1
- One Solution: Graph 2
- Infinitely Many Solutions: Graph 3
Steps to Solve
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Identify Graphs Examine each of the three graphs to understand their relationships to one another.
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Determine Solution Types Categorize the graphs based on the following criteria:
- No Solutions: The lines are parallel and never intersect.
- One Solution: The lines intersect at exactly one point.
- Infinitely Many Solutions: The lines coincide completely, representing the same line.
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Analyze Each Graph
- Graph 1: Check if lines intersect or are parallel.
- Graph 2: Repeat the analysis for this graph.
- Graph 3: Evaluate similarly.
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Classify Each Graph Based on the analysis, place each graph into the correct category (No Solutions, One Solution, Infinitely Many Solutions).
- No Solutions: Graph 1
- One Solution: Graph 2
- Infinitely Many Solutions: Graph 3
More Information
The three solution categories correspond to different linear relationship types in a system of equations. Understanding these relationships is crucial for solving linear equations and systems.
Tips
- Confusing parallel lines (which indicate no solutions) with lines that intersect (which indicate one solution).
- Overlooking coinciding lines (which indicate infinitely many solutions) when analyzing graphs.
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