The inequalities are 2x – y > 1 and x – 2y < –1
(i) Let us draw the graph of line
l1 : 2x – y = 1, passes through (

1

2

,0) and (0, –1) which is represented by AB.

Consider the inequality 2x – y > 1.
Putting x = y = 0, we get 0 > 1, which is false.
Therefore, origin does not lie in region of 2x – y > 1 i.e., 2x – y > 1 represents the area below the line AB excluding all the points lying on 2x – y = 1.
(ii) Let us draw the graph of the line
l2 : x – 2y = –1, passes through (–1, 0) and (0, 1/2) which is represented by CD.
Consider the inequality x – 2y < –1
Putting x = y = 0, we have 0 < –1, which is false.
Therefore, origin does not lie in region of x – 2y < –1 i.e., x – 2y < –1 represents the area above the line CD excluding all the points lying on x – 2y = –1
⇒ The common region of both the inequality is the shaded region as shown in figure.