SOLUTION: Graph y>2x+1 and 2x+y>2

First graph only the first boundary line, which is the
first inequality with the > replaced by =.  That is the
line whose equation is y = 2x + 1

So we draw the graph of the first boundary line by getting 
a couple of points.  We draw a GREEN dotted line through them, 
dotted because of the >.  (If it had been > we would 
have drawn the boundary line solid.)



Before we draw the other boundary line, we must
decide which side of the line the final shading
must be on.  To do this we choose any point which 
is not on the line as a test point.  Let's 
arbitrarily choose (3,3) on the right side of the
line as a test point. Substitute x=3, y=3 into the 
original inequality:

y > 2x+1
3 > 2(3)+1
3 > 6+1
3 > 7

This is FALSE, so we shade the OPPOSITE side of
the line from which (3,3) is on, which is
the LEFT side of the GREEN line.

Next we graph the second boundary line, which is the
second inequality with the > replaced by =. 

2x + y = 2

So we draw the graph of the second boundary line by getting 
a couple of points.  We draw a BLUE dotted line through them,
dotted because of the >.  (Again, if it had been > we 
would have drawn the boundary line solid.)



As before must decide which side of the BLUE line 
the final shading must be on.  To do this we choose 
any point which is not on the BLUE line as a test 
point.  Let's arbitrarily choose (4,2) on the right 
side of the BLUE line as a test point. Substitute 
x=4, y=2 into the original inequality:

    2x + y > 2
2(4) + (2) > 2
     8 + 2 > 2
        10 > 2


This is TRUE, so we DO shade the side of
the BLUE line which (4,2) lie on, which is
the RIGHT side of the BLUE line.
  
So we must shade the V-shaped wedge which is
LEFT of the GREEN line and RIGHT of the BLUE
LINE, as indicated below:



Edwin