The inequalities are x + y ≥ 4, 2x – y > 0 (i) The line $l_1$ : 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 $l_2$ : 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.