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

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The inequality to be graphed is: 2x - y >= 4

2x - y >= 4

=> y <= 2x - 4

The graph of the line 2x - y = 4 is shown below.

The region that satisfies the inequality 2x - y >= 4 is made up of the points that lie on the line and the region that lies below the line.

The next inequality is: 4x-2y<-2

4x - 2y < -2

=> 2y > 4x + 2

=> y > 2x + 1

The points that satisfy the given inequality lie above the line that has been drawn.

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].**

When graphing inequalities, there are two main things to do: Solve the inequality for y (helps with graphing the boundary), and using the inequality symbol (to help with shading).

Let's look at the first inequality: 2x-y>=4. Solve this inequality for y.

2x-y>=4 subtract 2x

-y>=-2x+4 Multiply by -1 (remember to flip the inequality symbol)

y<=2x-4

Now that the inequality is in slope-intercept form, graph the boundary as if it were a line. The inequality symbol indicates it is a solid line, and shaded below. Follow the same procedure with the second inequality:

4x-2y<-2 subtract 4x

-2y<-4x-2 divide by -2 (change signs = flip the symbol)

y>2x+1

This line will be dashed, and will be shaded above.

When you graph both inequalities on the same plane, the overlapping region represents the set of solutions to this system of inequalities.

Hope that helped!