https://file.aiquickdraw.com/mathbot/file/17233084471764kmcqxmp.jpg

To solve this problem, we need to determine how many times the linear equation intersects with the quadratic equation, which are both represented graphically.

### Steps to solve:

1. **Identify the Equations:**
   - The graph shows a parabola representing the quadratic equation.
   - The graph also shows a line representing the linear equation.

2. **Determine the Number of Intersections:**
   - The solutions to the system of equations correspond to the points where the line intersects the parabola.
   - By looking at the graph, we can see how many points the line crosses the parabola.

### Analysis:
- From the image, it is clear that the line intersects the parabola at **two points**.

### Conclusion:
- Therefore, the system of equations has **two solutions**.

The correct answer is **C. 2**.

Would you like more details or have any further questions? 

Here are some related questions for further exploration:

1. How do you find the points of intersection algebraically between a quadratic and linear equation?
2. What does the discriminant tell us about the number of solutions in a quadratic equation?
3. How can you solve a system of equations graphically?
4. What are the different possible scenarios for the intersection of a line and a parabola?
5. How do you derive the equation of a parabola given a graph?
6. What is the significance of the vertex in a parabola?
7. How do transformations affect the graph of a quadratic function?
8. What are the key characteristics of linear and quadratic equations?

**Tip:** When solving graphically, always check the number of intersection points to determine the number of solutions in a system of equations.

Explore the graphical solution method for determining the number of intersections between linear and quadratic equations. This detailed analysis covers identifying equations from graphs and counting intersection points. Ideal for high school students studying algebra and graphical methods of solving equations.

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