The question in the image asks to "determine the system of inequalities from the solution region shown."

Step-by-Step Process:

1. Identifying the boundary lines:

   • There are two lines in the graph. Let's find their equations based on the given points.

   First line (left side):

   • Passes through the points (0, 10) and (10, 0).
   • The slope $m = \frac{0 - 10}{10 - 0} = -1$.
   • Using the point-slope form of the line equation $y = mx + c$, with $m = -1$ and the intercept $c = 10$, the equation is: $y = -x + 10$

   Second line (right side):

   • Passes through the points (0, 1) and (5, 0).
   • The slope $m = \frac{0 - 1}{5 - 0} = -\frac{1}{5}$.
   • Using the point-slope form with $m = -\frac{1}{5}$ and intercept $c = 1$, the equation is: $y = -\frac{1}{5}x + 1$

2. Inequalities based on the shaded region:

   • The shaded region is below both of these lines.

   • For the first line $y = -x + 10$, the shaded region is below the line, so the inequality is: $y \leq -x + 10$

   • For the second line $y = -\frac{1}{5}x + 1$, the shaded region is also below the line, giving the inequality: $y \leq -\frac{1}{5}x + 1$

3. Non-negative constraints:

   • The region is only in the first quadrant, so the constraints on the variables are: $x \geq 0, \quad y \geq 0$

Final System of Inequalities: