the graph that represents the solution of the set of inequalities is in option A
How to verify the option
To verify we pick a point in the solution area of option A and substitute into the inequality.
The chosen point should be peculiar to option A
Choosing the origin (0, 0)
x + y < 1
x - y ≤ 2
For x = 0 nd y = 0
0 + 0 < 1
0 < 1 - this is a solution
then for x - y ≤ 2
0 + 0 ≤ 2
0 ≤ 2 - this is a solution