Find the solutions of following inequalities graphically in a two dimensional plane. x - y < 2

x - y = 2 ...(i)

Putting x = 0, y - -2, therefore the point on th y-axis is (0, -2). The point on the x-axis is (-2,0' AB is the graph of (i).

Putting x = 0, y = 0 in the given inequality, w have 0 - 0 < 2 or 0 < 2', which is true. Hence origin lies in the half plane region I.

Clearly, all the points on the line satisfy the given inequality.

Hence, the shaded region I including the points on the line is the solution region of the inequality.