Find the solutions of following inequalities graphically in a two dimensional plane. 2x -3y>6.

2x - 3y = 6. ...(i)

Putting x = 0, y = -2, therefore the point on the y-axis is (0, -2).

The point on the jc-axis is (3,0). AB is the graph

Putting x = 0, y = 0 in the given inequality, w< have 2(0) - 3(0) > 6 or 0 > 6, which is false. Hence origin does not lie in the half plane region I.

Clearly any point on the line does not satisfy the given inequality. Hence the shaded region II excluding the points on the line is the solution region of the inequality.