From the figure, to find the system of inequalities associated with it:
Since the intercepts x and y are, (2,0) and (0,2)
So, the equation of the line is,
![x+y=2](https://img.qammunity.org/2023/formulas/mathematics/high-school/i17fnineo2vc1apnvoas8asdcq6rdusj3z.png)
Since the shaded area is located above the solid line,
Therefore, the inequality is
![x+y\ge2](https://img.qammunity.org/2023/formulas/mathematics/college/t7rmfusre9y4nk9727j7wsv94uaadwho7r.png)
Hence, the correct option is C.