https://file.aiquickdraw.com/mathbot/file/17267611519215mado7jt.jpg

The system of equations provided is:

\[
y = -x + 1
\]
\[
x - 2y = 4
\]

To solve this graphically, you need to graph both equations on the coordinate plane and identify where they intersect.

### Steps:
1. **First Equation**: \( y = -x + 1 \)
   - This is already in slope-intercept form \( y = mx + b \), where \( m = -1 \) (slope) and \( b = 1 \) (y-intercept).
   - To graph: Start at \( (0, 1) \) on the y-axis, and use the slope of -1 (down 1 unit, right 1 unit) to plot additional points.

2. **Second Equation**: \( x - 2y = 4 \)
   - Rearrange this into slope-intercept form \( y = mx + b \):
   \[
   x - 2y = 4 \quad \Rightarrow \quad -2y = -x + 4 \quad \Rightarrow \quad y = \frac{1}{2}x - 2
   \]
   - Now, the slope is \( \frac{1}{2} \) and the y-intercept is \( -2 \).
   - To graph: Start at \( (0, -2) \) on the y-axis, and use the slope \( \frac{1}{2} \) (up 1 unit, right 2 units) to plot additional points.

### Intersection Point:
The solution to the system of equations is where the two lines intersect on the graph.

Would you like me to generate a visual graph of these equations or guide you further with the graphing?

Also, here are some related questions to explore:
1. How do you solve a system of equations algebraically?
2. What does the slope represent in a linear equation?
3. How does the graphical method compare to substitution or elimination methods?
4. What happens if the lines are parallel?
5. How do you identify the slope and y-intercept from any linear equation?

**Tip:** Always check if the system is consistent (intersects at a point), inconsistent (parallel), or dependent (same line) when solving graphically.

Solve the following system of equations graphically: y = -x + 1, x - 2y = 4.

Learn how to solve the system of linear equations y = -x + 1 and x - 2y = 4 graphically. This guide explains key concepts such as slope-intercept form and graphing techniques, suitable for students in Grades 8-10.

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