https://file.aiquickdraw.com/mathbot/file/1727825459098n9c2bnrf.jpg

The system of equations given in the image is:

\[
\begin{cases}
-x + 2y = 4 \\
y = \frac{1}{2}x + 2
\end{cases}
\]

To solve this system graphically:

1. **Equation 1:**
   \(-x + 2y = 4\) can be rewritten in slope-intercept form (i.e., \(y = mx + b\)):
   \[
   2y = x + 4 \quad \Rightarrow \quad y = \frac{1}{2}x + 2
   \]
   So, both equations are identical, meaning the two lines overlap.

2. **Conclusion:**
   Since the two equations represent the same line, the system has **infinitely many solutions**. This happens when every point on the line is a solution to both equations.

The solution should be marked as **infinitely many solutions**.

Do you want more details or have any questions?

### Related Questions:
1. How do you determine when a system of equations has no solution?
2. What does it mean graphically when two lines have infinitely many solutions?
3. Can a system of linear equations have exactly one solution? How can we identify it?
4. What is the significance of parallel lines in a system of equations?
5. How do you convert an equation into slope-intercept form?

**Tip:** Identical equations always imply that the system has infinitely many solutions.

Graph the system below and write its solution:

{-x + 2y = 4
 y = (1/2)x + 2}

Learn how to solve a system of linear equations by graphing. The system includes the equations -x + 2y = 4 and y = (1/2)x + 2, which result in infinitely many solutions. Suitable for students in Grades 8-10.

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