Consistent and inconsistent systems | Algebra II | Khan Academy

TL;DR

The system of linear equations is consistent because the two lines intersect, indicating at least one solution.

Transcript

Is the system of linear equations below consistent or inconsistent? And they give us x plus 2y is equal to 13 and 3x minus y is equal to negative 11. So to answer this question, we need to know what it means to be consistent or inconsistent. So a consistent system of equations. has at least one solution. And an inconsistent system of equations, as ... Read More

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.

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

• A consistent system of linear equations has at least one solution, while an inconsistent system has no solutions.

• Graphically, a consistent system can have intersecting lines or lines that are the same, while an inconsistent system has parallel lines.

• By graphing the given equations, it is evident that the lines intersect, confirming the consistency of the system.