For the first one...let's pick a point in the shaded region...I'll choose (-1, 6)
This point should satisfy all of the inequalities in any answer
Look at the third answer....we have that
6 - 6 ≤ -11 (-1) 6 + 3(-1) ≥ -4 -2(-1) + 3(6) > 15
0 ≤ 11 true 6 - 3 ≥ -4 2 + 18 > 15
3 ≥ -4 true 20 > 15 true
So.....this answer is the correct one
Second one
y + 3x ≥ 2 ⇒ y ≥ -3x + 2
y + 4 ≥ (1/2)x ⇒ y ≥ (1/2)x - 4
Look at the graph on the bottom left...note that (2,0) is a point in the shaded region
So...replacing these into the inequalities, we have that
0 ≥ -3(2) + 2 and 0 ≥ (1/2)(2) - 4
0 ≥ -6 + 2 0 ≥ 1 - 4
0 ≥ -4 true 0 ≥ -3 true
So.....this graph is the correct one