https://file.aiquickdraw.com/mathbot/file/1730315791243ptbga8jp.jpg

To solve this problem, let’s examine each inequality separately and how they affect the graph.

### Step 1: Analyzing the Inequalities
1. **First Inequality:** \( y < -x + 1 \)
   - This inequality has a boundary line \( y = -x + 1 \), which has a slope of -1 and a y-intercept of 1.
   - Since it’s a "<" inequality (strict inequality), the line \( y = -x + 1 \) should be **dashed** to indicate that points on the line are not included in the solution.
   - The shading for this inequality will be **below** the line, as \( y \) values less than \( -x + 1 \) satisfy the inequality.

2. **Second Inequality:** \( x - y \leq 2 \)
   - Rearranging this inequality, we get \( y \geq x - 2 \).
   - The boundary line for this inequality is \( y = x - 2 \), with a slope of 1 and a y-intercept of -2.
   - Since it’s a "≤" inequality (inclusive inequality), the line \( y = x - 2 \) should be **solid**, indicating that points on the line are included in the solution.
   - The shading for this inequality will be **above** the line, as \( y \) values greater than or equal to \( x - 2 \) satisfy the inequality.

### Step 2: Identifying the Correct Graph
Now, we need to find a graph where:
- The region below the dashed line \( y = -x + 1 \) is shaded.
- The region above the solid line \( y = x - 2 \) is shaded.
- The solution set (overlap of the shaded regions) is correctly represented.

### Conclusion
Looking at the options provided:
- **Option B** is the correct graph, as it shows the shaded region below the dashed line \( y = -x + 1 \) and above the solid line \( y = x - 2 \). 

Thus, the answer is **(B)**.

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

### Related Questions
1. How would the solution region change if both inequalities were strict inequalities?
2. How does shading below or above the line affect the solution region in a graph?
3. What is the effect of changing the slope on the boundary line of a linear inequality?
4. How do solid and dashed lines help differentiate between inclusive and strict inequalities?
5. Can you describe the intersection of solution regions for systems of inequalities in different quadrants?

### Tip
When graphing inequalities, remember that **dashed lines** represent strict inequalities (without equality), while **solid lines** indicate inclusive inequalities (with equality). This helps clearly indicate whether points on the line are part of the solution.

Aubrey graphed the following system of linear inequalities. Which graph best represents the solution set to this system of inequalities? The system is: y < -x + 1 and x - y ≤ 2.

Explore how to solve and graph the system of linear inequalities y < -x + 1 and x - y ≤ 2. Learn the steps to determine which region satisfies both inequalities and how dashed and solid lines are used to represent solutions. Ideal for students in Grades 8-10.

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