https://file.aiquickdraw.com/mathbot/file/1726175235322286arnck.jpg

In the image you provided, the shaded region represents the solution to a system of linear inequalities. I will determine the inequalities based on the graph.

### Steps to identify the inequalities:
1. **Identify the boundary lines**:
   - There are two boundary lines, one vertical and one slanted.
   - The slanted line has a negative slope and intersects the y-axis above the origin.
   - The vertical line appears to be located at \( x = 1 \).

2. **Determine the equations of the lines**:
   - The vertical line is straightforward: it is \( x = 1 \).
   - The slanted line appears to pass through points like \( (0, 3) \) and \( (3, 0) \). This gives a slope of \( -1 \), so its equation is \( y = -x + 3 \).

3. **Determine the inequality signs**:
   - The shading on the left side of \( x = 1 \) means the inequality for this boundary is \( x \leq 1 \).
   - The shading above the slanted line suggests the inequality is \( y \geq -x + 3 \) because the shading is above the line.

### Final System of Inequalities:
1. \( x \leq 1 \)
2. \( y \geq -x + 3 \)

Would you like more details or have further questions? Here are some related questions:

1. How do we graph inequalities like these manually?
2. How can we verify if a point is a solution to this system?
3. What changes if the inequality were strict, like \( x < 1 \)?
4. Can inequalities have different boundary types (e.g., dashed lines)?
5. How do we interpret systems with more than two inequalities?

**Tip**: Always test a point (like the origin) when determining the correct region to shade for an inequality.

Identify the system of inequalities from the graph.

Learn how to solve a system of linear inequalities from a graph, with key algebraic concepts such as identifying boundary lines, determining inequalities, and interpreting shaded regions. This problem involves graphing techniques suitable for Grades 8-10.

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