What is the intersection of these two equations
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What is the intersection of these two equations

[From: ] [author: ] [Date: 11-05-02] [Hit: ]
a bunch of craziness! I know I gotta solve and substitute, but Im getting lost.. please help-You solved for y for the second equation.Great move.......
326. 2y^2 = x^2 - 2 and xy = 2

I solved for y in the second equation and got y = 2/x.
Then I substituted that into the first and got... a bunch of craziness! I know I gotta solve and substitute, but I'm getting lost.. please help

-
You solved for y for the second equation. Great move. Substitute that for the first equation and solve for x.

2(2/x)² = x² - 2
2(4/x²) = x² - 2
x²[8/x² = x² - 2] [Multiply both sides by x²]
8 = x^4 - 2x²
0 = x^4 - 2x² - 8 [Rearrange the terms]
0 = (x² - 4)(x² + 2)
x² - 4 = 0 and x² + 2 = 0
x² = 4 and x² = -2
x = ±2 [No solutions for x² + 2 = 0 and they are imaginary; ±i√2. Also; there are no real numbers for determining x² = -2]

Finally, substitute each of the x values for the second equation and solve for y.

When x = 2:

y = 2/2
y = 1

When x = -2:

y = 2/-2
y = -1

Therefore, the solution are (2,1) and (-2, -1)

I hope this helps!
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