X + y ≤ 9 …………………….. (1)
y > x …………………... (2)
x ≥ 0 …………………... (3)
The graph of the lines, x + y= 9 and y = x, are drawn in the figure below.
Inequality (1) represents the region below the line, x + y = 9 (including the line x + y = 9). It is observed that (0, 1) satisfies the inequality, y > x. [1 > 0] Therefore, inequality (2) represents the half plane corresponding to the line, y = x, containing the point (0, 1) [excluding the line y = x]. Inequality (3) represents the region on the right hand side of the line, x = 0 or y-axis (including y-axis).
Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the lines, x + y = 9 and x = 0, and excluding\ the points on line y = x as follows.
