Solution:
The given inequalities are \[x+y\le 9\], \[y>x\] , \[x\ge 0\]
For \[x+y\le 9\],
Let us put value of \[x=0\] and \[y=0\] in equation one by one, we get
\[y=9\] and \[x=9\]
We get the required points as \[(0,9)\] and \[(9,0)\]
To check if the origin is included in the line`s graph \[(0,0)\]
\[0\le 9\] Which is true, so the required area would be including the origin and hence will lie on the left side of the line`s graph.
For \[y>x\],Solving for \[y=x\]
We get \[x=0,y=0\]
hence the origin lies on the line`s graph.
We can take the other points as \[(0,0)\]and \[(2,2)\]
Now Checking for \[(9,0)\] in \[y>x\], We get,
\[0>9\]which is false, since the area would not include the area below the line`s graph and hence would be on the left side of the line.
Now we have \[x\ge 0\]
Therefore ,the area of the required line`s graph would be on the right side of the line`s graph.
In the below graph the shaded area in the graph is the required solution of the given inequalities.
