The first inequality is $2x-y >1$
Consider the equation $2x -y =1$
The points $(0,-1), (1,1)$ satisfy the equation.
The graph of the line using dotted lines is shown in the diagram.
The line divides the XY plane into two half planes.
Consider the point (0,0)
We see that $2(0) -0 >1$
$0 > 1$ is false.
Thus the region represented by the inequality $2x -y >1$ is the upper half plane which does not contain the point (0,0) [excluding the line 2x-y=1]
The second inequality is $x-2y <-1$
Consider the equation $x-2y=-1$
We see that the points $(-1,0) $ and $(1,1) satisfy the equation .
The graph of the line using dotted lines is shown in the diagram
Consider the point $(0,0)$
We see that $ 0-2(0) <-1$
$0 < -1$
The region represented by the inequality $x-2y <-1$ is the region to the right of the line $x-2y=-1$ (excluding the line x-2y=-1)
Step 3 :
Hence the solution of the given system of linear inequalities is represented by the common shaded region, including the points on the lines.