https://file.aiquickdraw.com/mathbot/file/17265148830439tful2ki.jpg

Refer to the illustration. Answer the questions.

How many solutions does the system of equations have?
Are the equations dependent or independent?


one solution, independent equations

two solutions, independent equations

infinite number of solutions, dependent equations

no solution, independent equations

no solution, dependent equations


The image shows two lines on a coordinate plane: one blue line and one pink line. They intersect at exactly one point. Based on this visual information, let's analyze the system of equations represented by these two lines.

- **Number of solutions**: Since the two lines intersect at exactly one point, the system has **one solution**.
- **Dependence or independence**: Since the lines are not parallel and intersect at one point, the equations are **independent**.

### Answer:
- **One solution, independent equations.**

Would you like more details, or do you have any questions?

### Related Questions:
1. How can you determine if two lines are parallel or perpendicular from their equations?
2. What is the slope of the blue line and the pink line in the graph?
3. How do you find the point of intersection of two lines algebraically?
4. What is the significance of independent equations in a system of linear equations?
5. How does the concept of dependent equations relate to the slopes of the lines?

**Tip**: Two lines are independent if they have different slopes, ensuring they intersect at one point.

Refer to the illustration. Answer the questions. How many solutions does the system of equations have? Are the equations dependent or independent?

Analyze a system of linear equations represented by two lines on a graph. Learn how to determine the number of solutions and whether the equations are dependent or independent. Suitable for high school students in Grades 9-11.

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