SOLUTION: Solve the following equation. Nonlinear equations 1. {x + y = 3 {x² + y² = 2

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Question 1182047: Solve the following equation. Nonlinear equations
1. {x + y = 3
{x² + y² = 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
x+%2B+y+=+3....eq.1
x%5E2+%2B+y%5E2+=+2.....eq.2
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x+%2B+y+=+3....eq.1, solve for x
x+=+3-y....eq.1a
go to
x%5E2+%2B+y%5E2+=+2.....eq.2, substitute x
%283-y%29%5E2+%2B+y%5E2+=+2.........solve for y
9-6y%2By%5E2+%2B+y%5E2+=+2
2y%5E2-6y%2B9-2++=0
2y%5E2-6y%2B7++=0
2y%5E2-6y%2B7++=0
using quadratic formula we get
y+=+%281%2F2+%29%283+%2B+i+%2Asqrt%285%29%29
y+=+%281%2F2+%29%283+-+i%2A+sqrt%285%29%29
go to
x+=+3-y....eq.1a, substitute y
x+=+3-%281%2F2+%29%283+%2B+i+%2Asqrt%285%29%29=>x+=+3%2F2+-+%28i%2Asqrt%285%29%29%2F2
x+=+3-%281%2F2+%29%283+-+i+%2Asqrt%285%29%29=>x+=+3%2F2+%2B+%28i%2Asqrt%285%29%29%2F2