SOLUTION: Solve each system by using the substitution method. 2x^2 - y^2 = 14 y - 2x = -4

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Question 839884: Solve each system by using the substitution method.
2x^2 - y^2 = 14
y - 2x = -4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The intersection of a straight line and a hyperbola,
1.2x%5E2+-+y%5E2+=+14
2. y+-+2x+=+-4
From eq. 2,
y=2x-4
Substitute into eq. 1,
2x%5E2-%282x-4%29%5E2=14
2x%5E2-%284x%5E2-16x%2B16%29=14
2x%5E2-4x%5E2%2B16x-16=14
-2x%5E2%2B16x-30=0
x%5E2-8x%2B15=0
%28x-5%29%28x-3%29=0
Two solutions:
x-5=0
x=5
Then, y=2x-4=2%285%29-4=10-4=6(5,6)
and
x-3=0
x=3
Then, y=2x-4=2%283%29-4=6-4=2(3,2)
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