The task asks to solve a system of equations by graphing, with the following equations:

1. $x - y = 1$
2. $y = -2x + 5$

Step 1: Rewrite the first equation in slope-intercept form ($y = mx + b$):

$x - y = 1 \quad \text{Rearrange to solve for } y:$ $y = x - 1$

Now we have two equations:

• $y = x - 1$ (red line)
• $y = -2x + 5$ (green line)

Step 2: Graph these equations

• For $y = x - 1$:

  • Start at the y-intercept ($b = -1$), so the point (0, -1).
  • Use the slope $m = 1$ (rise over run = 1/1):
    • From (0, -1), move up 1 unit and right 1 unit to (1, 0).
    • Plot more points if needed (e.g., (2, 1)).

• For $y = -2x + 5$:

  • Start at the y-intercept ($b = 5$), so the point (0, 5).
  • Use the slope $m = -2$ (rise over run = -2/1):
    • From (0, 5), move down 2 units and right 1 unit to (1, 3).
    • Plot more points if needed (e.g., (2, 1)).

Step 3: Find the intersection point

The solution to the system of equations is where the two lines intersect. By substitution or graphing, the intersection occurs at:

$x = 2, \; y = 1$

Final Answer:

The solution is: $(2, 1)$

Would you like me to provide more details on the process or graph the equations explicitly?

Here are 5 questions to deepen your understanding:

1. How do you rearrange equations into slope-intercept form?
2. What is the significance of the slope in graphing a line?
3. How can substitution confirm the solution to a system of equations?
4. Why is graphing a useful method to solve a system of equations?
5. How would you solve this system algebraically (e.g., elimination method)?

Tip: Always label your axes and choose points carefully when plotting graphs for clarity.