Solution:

The given inequalities are \[2x+y\ge 8\], \[x+2y\ge 10\]

For \[2x+y\ge 8\]

Let us put value of \[x=0\]and \[y=0\]in equation one by one, we get

\[y=8\]and \[x=4\]

We get the required points as \[(0,8)\] and \[(4,0)\]

To check if the origin is included in the line`s graph \[(0,0)\]

We get \[0\ge 8\], which is false

Therefore, the origin is not included in the solution area

Hence, the requires area would be the area to the right of line`s graph.

For \[x+2y\ge 10\]

Let us put value of \[x=0\]and \[y=0\]in equation one by one, we get

\[y=5\] and \[x=10\]

We get the required points as \[(0,5)\] and \[(10,0)\]

To check if the origin is included in the line`s graph \[(0,0)\]

We get \[0\ge 10\]which is false,

Therefore, the origin would not lie in the required solution area.

Hence the required area would be to the left of the line graph.

In the below graph the shaded area in the graph is the required solution of the given inequalities.