SOLUTION: x^2 + y^2 <= 1 (x-1)^2 + y^2 <= 1 Is it possible to find x and y?

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Question 174571: x^2 + y^2 <= 1
(x-1)^2 + y^2 <= 1
Is it possible to find x and y?
Found 2 solutions by ankor@dixie-net.com, Fombitz:
Answer by ankor@dixie-net.com(12692) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 <= 1
(x-1)^2 + y^2 <= 1
---------------------subtraction eliminates y^2
x^2 - (x-1)^2 <= 0
Foil
x^2 - (x^2 - 2x + 1) =< 0
Remove brackets
x^2 - x^2 + 2x - 1 =< 0
2x - 1 =< 0
2x =< + 1
x =< .5
:
Find y using x^2 + y^2 =< 1
.5^2 + y^2 =< 1
.25 + y^2 =< 1
y^2 =< 1 -.25
y^2 =< .75
y =< +/-sqrt%28.75%29
y =< .866
y => -.866

Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
First graph,
x%5E2+%2B+y%5E2+%3C=+1
That's a circle centered at (0,0) with a radius of 1.
Including all of the interior points.
drawing%28+300%2C+300%2C+-3%2C+3%2C+-3%2C+3%2Cgrid%281%29%2Ccircle%280%2C0%2C.1%29%2Ccircle%280%2C0%2C.2%29%2Ccircle%280%2C0%2C.3%29%2C%0D%0Acircle%280%2C0%2C.4%29%2C%0D%0Acircle%280%2C0%2C.5%29%2C%0D%0Acircle%280%2C0%2C.6%29%2C%0D%0Acircle%280%2C0%2C.7%29%2C%0D%0Acircle%280%2C0%2C.8%29%2C%0D%0Acircle%280%2C0%2C.9%29%2C%0D%0Acircle%28+0%2C+0%2C+1+%29%29
Next graph,
%28x-1%29%5E2+%2B+y%5E2+%3C=+1
That's a circle centered at (1,0) with a radius of 1.
Including all of the interior points.
drawing%28+300%2C+300%2C+-3%2C+3%2C+-3%2C+3%2Cgrid%281%29%2Ccircle%281%2C0%2C.1%29%2Ccircle%281%2C0%2C.2%29%2Ccircle%281%2C0%2C.3%29%2C%0D%0Acircle%281%2C0%2C.4%29%2C%0D%0Acircle%281%2C0%2C.5%29%2C%0D%0Acircle%281%2C0%2C.6%29%2C%0D%0Acircle%281%2C0%2C.7%29%2C%0D%0Acircle%281%2C0%2C.8%29%2C%0D%0Acircle%281%2C0%2C.9%29%2Ccircle%281%2C0%2C1%29%29
When you put those two together,
the region that satisfies both equations is the football shaped section in between the two circles.
drawing%28+300%2C+300%2C+-3%2C+3%2C+-3%2C+3%2C%0D%0Agreen%28line%28.5%2C.75%2C.5%2C-.75%29%29%2C%0D%0Agreen%28line%28.35%2C.55%2C.35%2C-.55%29%29%2C%0D%0Agreen%28line%28.2%2C.35%2C.2%2C-.35%29%29%2C%0D%0Agreen%28line%28.1%2C.2%2C.1%2C-.2%29%29%2C%0D%0Agreen%28line%28.65%2C.55%2C.65%2C-.55%29%29%2C%0D%0Agreen%28line%28.8%2C.35%2C.8%2C-.35%29%29%2C%0D%0Agreen%28line%28.9%2C.2%2C.9%2C-.2%29%29%2C%0D%0Agrid%281%29%2Ccircle%280%2C0%2C1%29%2Ccircle%281%2C0%2C1%29%29