Consistent and inconsistent systems | Algebra II | Khan Academy | Summary and Q&A

TL;DR
The system of linear equations is consistent because the two lines intersect, indicating at least one solution.
Key Insights
- ❓ A consistent system of linear equations has at least one solution, while an inconsistent system has no solutions.
- 🫥 A consistent system can have intersecting lines or lines that are the same, while an inconsistent system has parallel lines.
- 📈 Graphing the equations helps visualize and determine whether the system is consistent or inconsistent.
- 🫥 It is not necessary to find the exact point of intersection; confirming that the lines intersect is enough to establish consistency.
Transcript
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Questions & Answers
Q: What does it mean for a system of linear equations to be consistent?
A consistent system of linear equations has at least one solution, which indicates that the lines represented by the equations intersect at some point.
Q: How can you determine if a system of linear equations is inconsistent?
An inconsistent system of linear equations has no solutions, meaning the lines represented by the equations do not intersect or are parallel.
Q: Can a consistent system of linear equations have two or more solutions?
No, a consistent system can only have one solution, whether it is a single point of intersection or lines that are the same.
Q: Is it necessary to find the point of intersection to determine if a system of linear equations is consistent?
No, it is not necessary to find the exact point of intersection. Confirming that the lines intersect is sufficient to determine consistency.
Summary & Key Takeaways
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A consistent system of linear equations has at least one solution, while an inconsistent system has no solutions.
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Graphically, a consistent system can have intersecting lines or lines that are the same, while an inconsistent system has parallel lines.
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By graphing the given equations, it is evident that the lines intersect, confirming the consistency of the system.
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