The question asks for the solution to the system of equations represented in the graph. This involves finding the points where the two curves intersect.

Analysis of the Graph

• The graph shows a parabola (opening downwards), which represents a quadratic equation.
• There's also a straight line intersecting this parabola, representing a linear equation.

Solution to the System

The points of intersection between the parabola and the line are the solutions to the system. By observing the graph:

• One intersection appears to be at $(1, 2)$.
• Another intersection appears to be at $(4, -1)$.

Conclusion

The solutions to this system are the points: $(1, 2) \quad \text{and} \quad (4, -1)$

These are the coordinates where both equations (the line and the parabola) hold true simultaneously.

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Related Questions

1. How can you find intersection points algebraically?
2. What would the equations of the parabola and line be?
3. How does the graph of a parabola relate to its equation?
4. What is the significance of the vertex in a parabolic equation?
5. How can systems of equations be solved using substitution or elimination?

Tip

Always check the coordinates carefully to confirm they satisfy both equations when finding points of intersection graphically.