Solve the following system of inequalities graphically:

2x – y >1, x – 2y < – 1

Given 2x – y >1………………1

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = -1 and x = 1/2 = 0.5

The points are (0,-1) and (0.5 , 0)

Checking for the origin, putting (0,0)

0 >1 , which is false

Hence the origin does not lie in the solution region. The required region would be on the right of the line`s graph.

x – 2y < – 1…………2

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 1/2 = 0.5 and x = -1

The required points are (0, 0.5) and (-1, 0)

Now checking for the origin, (0,0)

0 < -1 which is false

Hence the origin does not lies in the solution area, the required area would be on the left side of the line`s graph.

∴ the shaded area is the required solution of the given inequalities.