SOLUTION: x − y2 + 9 = 0 2x2 + y2 − 10 = 0 What are all possible solutions using the elimination method?

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Question 963937: x − y2 + 9 = 0
2x2 + y2 − 10 = 0
What are all possible solutions using the elimination method?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x-y%5E2%2B9=0
2x%5E2%2By%5E2-10=0
From eq. 2,
y%5E2=10-2x%5E2
Substitute into eq. 1,
x-%2810-2x%5E2%29%2B9=0
x-10%2B2x%5E2%2B9=0
2x%5E2%2Bx-1=0
%28x%2B1%29%282x-1%29=0
Two solutions:
x%2B1=0
x=-1
Then,
y%5E2=10-2%281%2F4%29
y%5E2=10-1%2F2
y%5E2=19%2F2
y=0+%2B-sqrt%2819%2F2%29
y=0+%2B-sqrt%2838%29%2F2
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2x-1=0
2x=1
x=1%2F2
Then,
y%5E2=10-2%281%2F2%29
y%5E2=9
y=0+%2B-+3
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(-1,2sqrt%282%29)
(-1,-2sqrt%282%29)
(1%2F2,sqrt%2838%29%2F2)
(1%2F2,-sqrt%2838%29%2F2)
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