SOLUTION: My work sheet says "Systems of Linear Inequalities" so hopefully somoene can help... IDK how to graph this or wat to even do... can you help me? y > 2x +3 ( the > is equal to or

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Question 198852: My work sheet says "Systems of Linear Inequalities" so hopefully somoene can help... IDK how to graph this or wat to even do... can you help me?
y > 2x +3 ( the > is equal to or greater than)
_
y < 1
And it says somethin about the dark portion of the graph is the answer....
I am no tlooking fo rthe answer but just a way that I can understyand in the 8th grade
THANKZ!!
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given system of inequalities


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


First lets graph the first inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
graph of

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 with the test point


Substitute (0,0) into the inequality

Start with the given inequality.


Plug in and


Multiply


Combine like terms.



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 with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
---------------------------------------------------------------


Now lets graph the second inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (simply draw a horizontal line through )
graph of
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 with the test point

Substitute (0,0) into the inequality
Plug in and
Simplify



Since this inequality is true, we simply shade the entire region that contains (0,0)


Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
---------------------------------------------------------------


So we essentially have these 2 regions:

Region #1
Graph of


Region #2
Graph of




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 (which is the solution set).
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