To determine how many solutions there are to the system of equations in the graph, we need to find how many points of intersection exist between the curves. Here's what we observe in the graph:

1. There are two curves shown in the graph:

   • A parabola opening upward.
   • A horizontal line.

2. The solutions to the system of equations correspond to the points where the parabola intersects the horizontal line.

Observation:

The graph shows that the parabola intersects the horizontal line at two points.

Conclusion:

The system of equations has two solutions, as there are two intersection points.

Would you like me to explain why intersections represent solutions in a system of equations or help with something else?

Related Questions:

1. What do the points of intersection represent mathematically?
2. Can a parabola intersect a horizontal line more than twice? Why or why not?
3. How can we determine the exact coordinates of the intersection points algebraically?
4. What happens if the horizontal line shifts vertically?
5. How do we classify the solutions geometrically?

Tip:

In systems of equations involving graphs, always look for the number of intersections to determine the number of solutions.