Need help with graphing the following. 2x-y>=4 4x-2y

We'll solve the 1st
inequality.

We'll shift y to the right and we'll subtract 4
both sides:

2x - 4>= y => y =< 2x -
4

The graph of the function y = 2x - 4 is a straight
line.

We'll calculate the intercepting points of the line
with x and y axis.

The line is intercepting x axis if
y=0

2x - 4 = 0 => 2x = 4 => x = 4/2 =>
x = 2

The intercepting point with x axis is
(2,0).

The line is intercepting y axis if
x=0

y = -4

The intercepting
point with y axis is (0,-4).

We'll solve the 2nd
inequality. We'll isolate y to the left side:

-2y <
-4x - 2

We'll divide by -2 both sides abd the sense of the
inequality will be reversed:

y> 2x +
1

The graph of the function is also a
line.

The line is intercepting x axis if
y=0

2x + 1 = 0

x =
-1/2

The intercepting point with x axis is
(-1/2,0).

The line is intercepting y axis if
x=0

y = 1

The intercepting
point with y axis is (0,1).

The
values of x that satisfy both inequalities of the system are found in the interval
(-1/2,2].