Represent the following inequalities graphically in a two dimensional plane. (1) x + y < 5

Putting y = 0, x - 5, therefore the point on the x-axis is (5,0). The point on the y-axis is (0, 5). AB is the graph of (i) (See Figure).

Putting x = 0, y = 0 in the given inequality, we have 0 + 0 < 5 or 5 > 0 which is true.

Hence, origin lies in the half plane region I.

Clearly, any point on the line does not satisfy the given inequality.

Hence, the shaded region 1 excluding the points on the line is the solution region of the inequality.