SOLUTION: How would you find the points that the graphs of the equation in the following systems have in common? x^2+y^2=4 x=y

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Question 89877: How would you find the points that the graphs of the equation in the following systems have in common?
x^2+y^2=4
x=y
Found 2 solutions by jim_thompson5910, checkley75:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28highlight%28x%29%29%5E2=4 Plug in y=x

2x%5E2=4 Combine like terms


x%5E2=2 Divide both sides by 2

x=0%2B-sqrt%282%29 Take the square root of both sides

So our solutions are (-sqrt%282%29,-sqrt%282%29) and (sqrt%282%29,sqrt%282%29)


Check:
%28sqrt%282%29%29%5E2%2B%28%28sqrt%282%29%29%29%5E2=4

2%2B2=4

4=4 works

or

%28-sqrt%282%29%29%5E2%2B%28%28-sqrt%282%29%29%29%5E2=4

2%2B2=4

4=4 works



We can also verify with this graph

drawing%28500%2C500%2C-6%2C6%2C-6%2C6%2C%0D%0Agraph%28500%2C500%2C-6%2C6%2C-6%2C6%2Cx%29%2C%0D%0Acircle%280%2C0%2C2%29%2C%0D%0Acircle%28sqrt%282%29%2Csqrt%282%29%2C0.05%29%2C%0D%0Acircle%28sqrt%282%29%2Csqrt%282%29%2C0.08%29%2C%0D%0Acircle%28-sqrt%282%29%2C-sqrt%282%29%2C0.05%29%2C%0D%0Acircle%28-sqrt%282%29%2C-sqrt%282%29%2C0.08%29%0D%0A%0D%0A%29

and if you used Pythagoreans theorem, you would verify your answer.

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST I WOULD PLOT THEM & SEE IF THERE IS ANY OBVIOUS SOLUTION.
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+x%2C+y%5E2+=+-x%5E2+%2B4%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = x and y^2 = -x^2
+4).
OR SET X=Y & SOLE FOR Y IN THE FIRST EQUATION
Y^2+Y^2=4
2Y^2=4
Y^2=4/2
Y^2=2
Y=+/-1.414 ANSWER.
X=Y=+/-1.414 ANSWER.