SOLUTION: How would you solve the substitution equation: x+y=1 X^2+xy-y^2=-1 Thank you.

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Question 681944: How would you solve the substitution equation:
x+y=1
X^2+xy-y^2=-1
Thank you.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=1...............1
x%5E2%2Bxy-y%5E2=-1........2
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x%2By=1...............1...solve for x
x=1-y.......substitute in 2
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x%5E2%2Bxy-y%5E2=-1........2
%281-y%29%5E2%2B%281-y%29y-y%5E2=-1.........solve for y
1-2y%2By%5E2%2By-y%5E2-y%5E2=-1
1-2y%2Bcross%28y%5E2%29%2By-cross%28y%5E2%29-y%5E2=-1
1-y-y%5E2=-1
1%2B1-y-y%5E2=0
y%5E2%2By-2=0...use quadratic formula
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29+
y+=+%28-1+%2B-+sqrt%28+1%2B8+%29%29%2F2+
y+=+%28-1+%2B-+sqrt%289%29%29%2F2+
y+=+%28-1+%2B-+3%29%2F2+
solutions:
y+=+%28-1+%2B3%29%2F2+
y+=+2%2F2+
y+=+1+
and
y+=+%28-1+-3%29%2F2+
y+=+-4%2F2+
y+=+-2+

now find x

if y+=+1+:
x=1-y
x=1-1
x=0

if y+=+-2+:
x=1-%28-2%29
x=1%2B2
x=3

so, solution pairs are:
1. y+=+1+ and x=0
2. y+=+-2+ and x=3