Word problem of Linear inequalities Questions in English

(A) To find the region satisfying the given inequalities:
$1$. For $y - x \geq 2$: The boundary line is $y = x + 2$. Testing the origin $(0,0)$, we get $0 - 0 \geq 2$, which is false. Thus, the region lies on the side of the line not containing the origin.
$2$. For $x + y \leq 5$: The boundary line is $x + y = 5$. Testing the origin $(0,0)$, we get $0 + 0 \leq 5$, which is true. Thus, the region lies on the side of the line containing the origin.
$3$. $x \geq 0$ and $y \geq 0$ restrict the region to the first quadrant.
$4$. Combining these, the region is a triangle bounded by the lines $y = x + 2$, $x + y = 5$, and the $y$-axis $(x=0)$.
$5$. Comparing this with the given options, the shaded region in image $A$ correctly represents this triangular area.