Answer
See below:
Work Step by Step
consider the provided inequalities,
\[x-y\ge -1\]and\[5x-2y\le 10\]
Replace each inequality symbol with an equal sign,
\[x-y=-1\]and\[5x-2y=10\]
Now, draw the graph of the equation\[x-y=-1\]:
Put \[y=0\] for x-intercept and \[x=0\] for y-intercept in the equation \[x-y=-1\].
So, the x-intercept is \[-1\] and y-intercept is \[1\].
Therefore, the line is passing through \[\left( -1,0 \right)\]and \[\left( 0,1 \right)\].
Now, consider a test point \[\left( 0,0 \right)\], which lies in the half-plane above the line.
Substitute \[x=0\] and \[y=0\]in \[x-y\ge -1\].
\[\begin{align}
& 0-0\ge -1 \\
& 0\ge -1
\end{align}\]
Since \[\left( 0,0 \right)\]satisfies the above inequality \[x-y\ge -1\].
So, the test point \[\left( 0,0 \right)\] is part of the solution set.
All the points on the same side of the line \[x-y=-1\]as the point \[\left( 0,0 \right)\] are members of the solution set.
Since,\[x-y\ge -1\] contains an equal sign.
So, the line should be solid.
Now, draw the graph of the equation\[5x-2y=10\]:
Put \[y=0\] for x-intercept and \[x=0\] for y-intercept in the equation \[5x-2y=10\].
So, the x-intercept is \[2\] and y-intercept is \[-5\].
Therefore, the line is passing through \[\left( 2,0 \right)\]and \[\left( 0,-5 \right)\].
Now, consider a test point \[\left( 0,0 \right)\], which lies in the half-plane above the line.
Substitute \[x=0\] and \[y=0\]in \[5x-2y\le 10\].
\[\begin{align}
& 5\cdot 0-2\cdot 0\le 10 \\
& 0\le 10
\end{align}\]
Since \[\left( 0,0 \right)\]satisfies the above inequality \[5x-2y\le 10\].
So, the test point \[\left( 0,0 \right)\] is part of the solution set.
All the points on the same side of the line \[5x-2y=10\]as the point \[\left( 0,0 \right)\] are members of the solution set.
Since,\[5x-2y\le 10\] contains an equal sign.
So, the line should be solid.
Therefore, the graph of the provided linear inequality is:
