SOLUTION: Solve the system and graph the curves: e) x^2+y^2 = 2 ;and x-y = 4

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Question 1048631: Solve the system and graph the curves:
e) x^2+y^2 = 2 ;and
x-y = 4
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve the system and graph the curves:
x^2+y^2 = 2 ;and
x-y = 4
~~~~~~~~~~~~~~~~~~~~ 

x%5E2%2By%5E2 = 2,     (1)
x-y = 4          (2)

Express x = 4 + y from (2) and substitute it into (1). You will get

%284+%2By%29%5E2+%2B+y%5E2 = 2,  or

16+%2B+8y+%2B+y%5E2+%2B+y%5E2 = 2,  or

2y%5E2+%2B+8y+%2B+14 = 0,  or

y%5E2+%2B+4y+%2B+7 = 0.

Apply the quadratic formula. You will get

y%5B1%2C2%5D = %28-4+%2B-+sqrt%28%28-4%29%5E2+-+4%2A7%29%29%2F2 = %28-4+%2B-+sqrt%28-12%29%29%2F2.

There are no real solutions.

See the plot


Plots y = sqrt%282-x%5E2%29, y = -sqrt%282-x%5E2%29 (red+green) and y = x-4 (blue).