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.