To solve the simultaneous equations from the graph, we look for the point where the two lines intersect.

The equations are:

1. $y = -2x + 4$
2. $y = \frac{1}{2}x + 1$

From the graph, we can visually find the point of intersection. It appears the two lines meet at $(x, y) = (1, 3)$.

Thus, the solution to the system of equations is: $x = 1, \quad y = 3$

Would you like a more detailed breakdown or have any further questions?

Here are some related questions you can explore:

1. How would you solve this system algebraically?
2. What are other methods for solving simultaneous equations (like substitution or elimination)?
3. How do you check the solution of a system of equations?
4. What does the graph of a system of linear equations represent geometrically?
5. How does the slope of each line relate to the coefficients in the equations?

Tip: Always check the solution by substituting the values back into both original equations to verify they hold true!