To answer the question about which graph shows a system of equations with infinitely many solutions, we need to identify when two lines on a graph are the same line. This occurs when the equations of the lines are the same, meaning they overlap perfectly.

Criteria for Infinite Solutions:

• The lines must have the same slope.
• The lines must intersect at every point (i.e., they are the same line).

Analyzing the Graphs:

From the provided image, the graph in the bottom left corner shows two lines that overlap completely, which indicates that they represent the same equation. This means the system of equations has infinitely many solutions.

Conclusion:

The bottom-left graph represents a system of equations with infinitely many solutions.

Would you like further details or have any questions about this? Here are 5 related questions to explore:

1. What are the conditions for a system of equations to have no solution?
2. How can you algebraically determine if a system has infinitely many solutions?
3. What is the difference between coincident lines and parallel lines?
4. How can you express the solution of a system with infinitely many solutions?
5. How does the graphical method compare to substitution or elimination in solving systems?

Tip: When two lines have identical equations, their graphs will coincide, resulting in infinitely many solutions.