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Question 42857: Find the exact solution(s) of the system: (x^2/4)-y^2=1 and x=y^2+1.
Thank You
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! We can actually solve this system by substitution...let me show you...from
(x^2/4) - y^2 = 1 and x = y^2 + 1 we can move the y^2 in the left equation to the other side and get
(x^2/4) = y^2 + 1
but we know from the second equation, that that equals x, so we have
(x^2/4) = x
x^2 = 4x
x^2 - 4x = 0
x(x - 4) = 0
x = 0 or x = 4
Now we plug these into the equations to find y...
In turns out that there are no solutions for x = 0, but there are for x = 4...
4 = y^2 + 1
y^2 = 3
y = ± sqrt(3)
so our two solutions are
(4, sqrt(3)) and (4, -sqrt(3))
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