The images provided show graphs of different lines, and you're asked to match each graph with the correct number of solutions (one solution, no solution, or infinitely many solutions).

Let's break down each graph:

1. First graph: The green and blue lines intersect at a single point, which means there is one solution.

2. Second graph: The green and blue lines are parallel and do not intersect, meaning there are no solutions.

3. Third graph: The green and blue lines overlap perfectly, indicating that they are the same line. This means there are infinitely many solutions because every point on the line satisfies both equations.

Answers:

1. First graph: One solution
2. Second graph: No solution
3. Third graph: Infinitely many solutions

Let me know if you need further clarification!

Follow-up Questions:

1. How do parallel lines relate to the concept of no solution in systems of linear equations?
2. Can you describe what happens when two lines intersect at more than one point?
3. What is the geometric interpretation of a system of equations with infinitely many solutions?
4. How can the slope and y-intercept of two lines determine if they are parallel, intersecting, or identical?
5. What is the significance of the point of intersection in a system of equations?

Tip: When you have two linear equations, their slopes and y-intercepts directly determine if the lines intersect, are parallel, or are identical.