Replace each point in both inequalities and see if the inequality remains:
(0,1) = (x,y)
1 ≥ 1/3(0)-2
1≥-2
y>4/3x+1
1>4/3(0)+1
1>1 NOT TRUE.
Point b.
(1,0) = (x,y)
0 ≥ 1/3(1)-2
0≥ 1/3-2
0≥-5/3
0>4/3(1)+1
0>7/3 NOT TRUE
Pint c. (-3,2)
2≥1/3(-3)-2
2≥ -1-2
2≥-3
2>(4/3)-3+1
2>-4+1
2>-3 TRUE
(-3,2) is a solution point to the set of inequalities. (option c)