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.