In this problem, we are asked to determine which graph represents a system of equations that has no solution.

For a system of equations to have no solution, the lines must be parallel. This occurs when the two lines have the same slope but different y-intercepts, which means they will never intersect.

Now, let's analyze each graph:

• Option A: The two lines intersect at one point. This system has exactly one solution, so it's not the correct choice.
• Option B: The two lines are parallel (same slope, different y-intercepts). This system has no solution because the lines will never intersect. This is a likely candidate.
• Option C: The two lines intersect at one point. This system has exactly one solution, so it's not the correct choice.
• Option D: The two lines intersect at one point. Again, this system has exactly one solution, so it's not the correct choice.

The correct answer is Option B, where the lines are parallel and thus have no solution.

Would you like more details or have any questions? Here are some related questions for further practice:

1. What does it mean for a system of equations to have infinitely many solutions?
2. How do you determine the slope of a line from its equation?
3. Can a system of equations have exactly two solutions? Why or why not?
4. What are some real-world examples of systems with no solution?
5. How do you graphically find the solution to a system of equations?

Tip: When solving systems of equations, always check if the lines are parallel (same slope) to quickly determine if there is no solution.