SOLUTION: What is the graph for xy>=0; how would I solve for y in this case? and the graph for y^2>x^2?

Algebra ->  Algebra  -> Inequalities -> SOLUTION: What is the graph for xy>=0; how would I solve for y in this case? and the graph for y^2>x^2?      Log On

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Question 340273: What is the graph for xy>=0; how would I solve for y in this case? and the graph for y^2>x^2?
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
Think about it.
First quadrant, x%3E0, y%3E0, xy%3E0
Second quadrant, x%3C0,y%3E0, xy%3C0
Third quadrant, x%3C0, y%3C0, xy%3E0
Fourth quadrant, x%3E0, y%3C0, xy%3C0
Also include the in the first and third quadrant and on the x and y axes.
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Solve for y%5E2=x%5E2
y=x and y=-x
That's two lines.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%2C-x%29
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Pick points in each region and test the inequality.
Since the "=" sign is not included the regions are broken up into 8 regions not just 4 regions, so use the two lines and the two axes to demarcate each region.

In the first region, x=4, y=2
y%5E2%3Ex%5E2
1%5E2%3E2%5E2
1%3E4
False, this region is not in the solution region.
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In the second region, x=2,y=4
y%5E2%3Ex%5E2
4%3E1
True, this region is part of the solution region.
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Continue until you've tested a point in each region.
Remember the x and y axes are not included in the solution region.