The inequalities are 2x + y ≥ 8 and x + 2y ≥ 10 (i) Let us draw the graph of the line $l_1$ : 2x + y = 8 passes through (4, 0) and (0, 8) which is represented by AB. Consider the inequality 2x + y ≥ 8 Putting x = y = 0, we get 0 ≥ 8, which is false. ∴ Origin does not lie in the region of 2x + y ≥ 8. i.e., 2x + y ≥ 8 represents the area above the line AB and all the points lying on 2x + y = 8. (ii) Let us draw the graph of line $l_2$ : x + 2y = 10, passes through (10, 0) and (0, 5) which is represented by CD. Consider the inequality x + 2y ≥ 10 Putting x = 0, y = 0, we have 0 ≥ 10, which is false. ∴ The origin does not lie in region of x + 2y ≥ 10 i.e., x + 2y ≥ 10 represents the area above the line CD and all the points lying on x + 2y = 10. ⇒ The common region of both the inequality is the shaded region as shown in the figure.