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The problem asks for the solutions to the system of equations involving the line \( y = -2x + 4 \) and the equation represented by the graph, which appears to be a quadratic function (parabola).

To solve this system graphically, we need to identify the points where the line intersects the parabola. The given options are:

1. \( (3, -2) \) and \( (4, 0) \)
2. \( (2, -2) \) and \( (1, 0) \)

### Steps:
1. **Line Equation:** The line is \( y = -2x + 4 \), which has a slope of \(-2\) and a y-intercept at \( (0, 4) \).
2. **Graph Analysis:** The parabola intersects the x-axis at \( (4, 0) \) and \( (1, 0) \), and has a vertex at approximately \( (2.5, -2) \).
3. **Intersection Points:**
   - Looking at the graph, the points where the line seems to intersect the parabola are around \( (2, -2) \) and \( (1, 0) \).

Thus, the solution to the system of equations is likely the points \( (2, -2) \) and \( (1, 0) \), making the correct answer:

\[
\boxed{(2, -2) \text{ and } (1, 0)}
\]

Would you like further clarification or a more detailed breakdown? Here are some related questions you could explore:

1. How can we algebraically solve for the points of intersection between a linear and quadratic equation?
2. How do we determine the equation of a parabola from a graph?
3. What are the key characteristics of a parabola that help in solving systems of equations?
4. How does the slope of a line affect where it intersects a parabola?
5. How do we graph systems of equations involving quadratic and linear equations?

**Tip:** Always check both graphical and algebraic methods when solving systems of equations for more accurate results.

What are the solutions to the system of equations composed of the line y = -2x + 4 and the equation represented in the graph?

Solve the system of equations involving the line y = -2x + 4 and a quadratic equation from the graph. Learn about the intersection points of a line and parabola with step-by-step guidance, covering key algebraic concepts. Suitable for students in Grades 8-10.

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