Let's look at the first inequality, x + y > 2
First of all, the boundary will be the line x + y = 2. This line is not part of the set so you will draw it as a dotted line. To draw the line, you can just find it's x and y intercepts and pass the line through them.
The whole solution set is on the same side of this line. To figure out which side, just pick a test point on each side. In this case, the (2,2) works. Thus the graph will be all points on the side that contains (2,2) so you can just shade that region in.
Now try this with the second inequality x - y < 2.
If you also want to graph the solution set of the system (region where both inequalities are simultaneously satisfied), you just draw the two boundary lines (dotted for < and >, or continuous for ≤ and ≥), and shade in the region that is common to the graphs of both inequalities.