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.