The inequalities are x + y ≤ 6 and x + y ≥ 4 (i) The line $l_1$ : x + y = 6 passes through (6, 0) and (0, 6). It is represented by AB. Consider the inequality x + y ≤ 6 Putting x = 0, y = 0 in x + y ≤ 6 0 < 6, which is true. ∴ Origin lies in the region of x + y ≤ 6 ∴ x + y ≤ 6 is represented by the region below the line x + y = 6 and all the points lying on it. (ii) The line l2 : x + y = 4 passes through (4, 0) and (0, 4). It is represented by CD. Consider the inequality x + y ≥ 4 Putting x = 0, y = 0 in x + y ≥ 4 or, 0 + 0 > 4, which is false. ∴ Origin does not lie in the region of x + y ≥ 4 ∴ x + y ≥ 4 is represented by the region above the line x + y = 4 and all the points lying on it. ∴ The solution region is the shaded region between AB and CD as shown in the figure.