The inequalities are x + y ≥ 4, 2x – y > 0
(i) The line l1 : x + y = 4 passes through (4, 0)
and (0, 4). This line is represented by AB.
Consider the inequality x + y ≥ 4
Putting x = 0, y = 0 in x + y ≥ 4, we get
0 ≥ 4, which is false.
Origin does not lie in this region.
Therefore, x + y ≥ 4 is represented by the region above the line x + y = 4 and all points lying on it.
(ii) The line l2 : 2x – y = 0 passes through (0, 0) and (1, 2).
This line is represented by CD.
Consider the inequality 2x – y > 0
Putting x = 1, y = 0, we get 2 > 0, which is true This shows (1, 0) lies in the region.
i.e. region lying below the line 2x – y = 0 represents 2x – y > 0
∴ The common region to both inequalities is shaded region as shown in the figure.