Question 340273
Think about it. 
First quadrant, {{{x>0}}}, {{{y>0}}}, {{{xy>0}}}
Second quadrant, {{{x<0}}},{{{y>0}}}, {{{xy<0}}}
Third quadrant, {{{x<0}}}, {{{y<0}}}, {{{xy>0}}}
Fourth quadrant, {{{x>0}}}, {{{y<0}}}, {{{xy<0}}}
Also include the {{{x and {{{y axes since the inequality includes the "=" sign.
So then {{{xy>=0}}} in the first and third quadrant and on the x and y axes.
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Solve for {{{y^2=x^2}}}
{{{y=x}}} and {{{y=-x}}}
That's two lines.
{{{graph(300,300,-10,10,-10,10,x,-x)}}}
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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.

{{{drawing(300,300,-10,10,-10,10,grid(1),circle(4,2,0.2),circle(2,4,0.2),graph(300,300,-10,10,-10,10,x),graph(300,300,-10,10,-10,10,-x))}}}

In the first region, {{{x=4}}}, {{{y=2}}}
{{{y^2>x^2}}}
{{{1^2>2^2}}}
{{{1>4}}} 
False, this region is not in the solution region.
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In the second region, {{{x=2}}},{{{y=4}}}
{{{y^2>x^2}}}
{{{4>1}}}
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.