SOLUTION: FInd the exact solution(s) of each system of equations x^2-y^2=-8 y=2x+1

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Question 840431: FInd the exact solution(s) of each system of equations
x^2-y^2=-8
y=2x+1

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The intersection of a line and a hyperbola,
1.x%5E2-y%5E2=-8
2.y=2x%2B1
Subsstitute eq. 2 into eq. 1,
x%5E2-%282x%2B1%29%5E2=-8
x%5E2-%284x%5E2%2B4x%2B1%29=-8
-3x%5E2-4x-1=-8
-3x%5E2-4x%2B7=0
3x%5E2%2B4x-7=0
%283x%2B7%29%28x-1%29=0
Two solutions:
3x%2B7=0
3x=-7
x=-7%2F3
Then
y=2%28-7%2F3%29%2B1
y=-14%2F3%2B3%2F3
y=-11%2F3
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.
.
x-1=0
x=1
Then
y=2x%2B1
y=2%281%29%2B1
y=3
(-7/3,-11/3) and (1,3)
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