The inequalities are x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
(i) l1 : x + 2y = 10 passes through (10, 0) and (0, 5). The line AB represents this equation.
Consider the inequality x + 2y ≤ 10 putting
x = 0, y = 0, we get 0 < 10 which is true.
∴ Origin lies in the region of x + 2y ≤ 10.
∴ Region lying below the line AB and the points lying on it represents x + 2y ≤ 10
(ii) l2 : x + y = 1 passes through (1, 0) and (0, 1). Thus line CD represents this equation. Consider the inequality x + y ≥ 1 putting x = 0, y = 0, we get 0 ≥ 1, which is not true. Origin does not lie in the region of x + y ≥ 1.
∴ The region lying above the line CD and the points lying on it represents the inequality x + y ≥ 1
(iii) l3 : x – y = 0, passes through (0, 0). This is being represented by EF. Consider the inequality x – y ≤ 0, putting x = 0, y = 1, We get 0 – 1 ≤ 0 which is true
⇒ (0, 1) lies on x – y ≤ 0
The region lying above the line EF and the points lying on it represents the inequality x – y ≤ 0.
(iv) x ≥ 0 is the region lying on the right of Y-axis and the points lying on x = 0.
(v) y ≥ 0 is the region above X-axis, and the points lying on y = 0.
∴ The shaded area in the figure represents the given inequalities.