Given:
[tex]x-y\le3[/tex][tex]x>-5[/tex]
Consider the equation of the first inquality.
[tex]x-y=3[/tex]
[tex]y=x-3[/tex]
Set x=0, we get
[tex]y=0-3=-3[/tex]
We get the point (0,-3).
Set x=3, we get
[tex]y=3-3=0[/tex]
We get the point (3,0).
Mark the points (0,-3) and (3,0) and draw a ray to join the points.
Let a point (0,0) from the left of the line that does not lie on the line.
substitute x=0, y=0 in the given inequality, we get
[tex]0-0\le3[/tex][tex]0\le3[/tex]
This is true so the point from the left side of the equation line on the inequality.
Now shade the left side of the line.
The next inequality is
[tex]x>-5[/tex]
Draw a dotted vertical line that parallels the y-axis at the point (-5,0).
And the values are greater than -5, so shade the right side of the line.
The graph is
The intersection of the coordinates is the grey shaded region.
The whole region lies between (-5,0),(-5,-8), (0,-3) and (3,0).
We can see that (0,0) is also the intersection of the given inequalities.
