SOLUTION: I am not good with graphing can you help Solve the following system of linear inequalities by graphing. x – 2y greater than and equal to 4 x less than and equal to 4

Algebra ->  Graphs -> SOLUTION: I am not good with graphing can you help Solve the following system of linear inequalities by graphing. x – 2y greater than and equal to 4 x less than and equal to 4       Log On


   

Question 88163: I am not good with graphing can you help
Solve the following system of linear inequalities by graphing.
x – 2y greater than and equal to 4
x less than and equal to 4
thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of inequalities
x-2y%3E=4
x%3C=4

In order to graph this system of inequalities, we need to graph each inequality one at a time.


First lets graph the first inequality x-2y%3E=4
In order to graph x-2y%3E=4, we need to graph the equation x-2y=4 (just replace the inequality sign with an equal sign).
So lets graph the line x-2y=4 (note: if you need help with graphing, check out this solver)

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%281%2F2%29x-2%29+ graph of x-2y=4
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality x-2y%3E=4 with the test point

Substitute (0,0) into the inequality
%280%29-2%280%29%3E=4 Plug in x=0 and y=0
0%3E=4 Simplify

Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of x-2y%3E=4 with the boundary (which is the line x-2y=4 in red) and the shaded region (in green)

---------------------------------------------------------------


Now lets graph the second inequality x%3C=4
In order to graph x%3C=4, we need to graph the equation x=4 (just replace the inequality sign with an equal sign).
So lets graph the line x=4 (note: if you need help with graphing, check out this solver)

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+1000%28x-4%29%29+ graph of x=4
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality x%3C=4 with the test point

Substitute (0,0) into the inequality
%280%29%3C=4 Plug in x=0 and y=0
0%3C=4 Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of x%3C=4 with the boundary (which is the line x=4 in red) and the shaded region (in green)

---------------------------------------------------------------


So we essentially have these 2 regions:

Region #1
Graph of x-2y%3E=4


Region #2
Graph of x%3C=4




When these inequalities are graphed on the same coordinate system, the regions overlap to produce this region. It's a little hard to see, but after evenly shading each region, the intersecting region will be the most shaded in.







Here is a cleaner look at the intersection of regions




Here is the intersection of the 2 regions represented by the series of dots