Solve the following systems of inequalities graphically 2x – y > 1, x – 2y < 1

x -2y < -1 …(ii)

Graph of inequality (i). Let us draw the graph of the line 2x - y = 1.

at y = 0, x = we get the point on x - axis

at x - 0, y = -1 we get the point (0, -1) on y-axis.

Putting x = y = 0 in (i) we get 0 > 1 which is false.

Hence, half-plane region not containing the origin is the solution region of the given inequality.

Graph of inequality (ii): Let us draw the graph of the line x - 2y = -1. At y = 0, x = -1, we get the point (-1,0) on x-axis.

At x = 0, y = , we get the point 10, - on y - axis.

Putting x = y = 0 in (ii) we get 0 < -1 which is false.

Hence, half-plane region not containing the origin is the solution region of the given inequality.

The common region of the above two regions represents the solution set of the given linear constraints.