SOLUTION: Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find more than one pair, then list your pairs in order by increasing x value, separated by comma

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find more than one pair, then list your pairs in order by increasing x value, separated by comma      Log On


   

Question 1077333: Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find more than one pair, then list your pairs in order by increasing x value, separated by commas.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
all pairs of real numbers (x,y) such that+x+%2B+y+=+6 and x%5E2+%2B+y%5E2+=+28
x+%2B+y+=+6+...solve for x
x+=+6+-y
substitute in x%5E2+%2B+y%5E2+=+28
%286-y%29%5E2+%2B+y%5E2+=+28.....solve for y
36-12y%2By%5E2+%2B+y%5E2+=+28
36-12y%2B2y%5E2++-28=0
2y%5E2-12y%2B36++-28=0....both sides divide by 2
y%5E2-6y%2B18++-14=0
y%5E2-6y%2B4=0.......complete square
%28y%5E2-6y%2Bb%5E2%29-b%5E2%2B4=0
%28y%5E2-6y%2B3%5E2%29-3%5E2%2B4=0
%28y-3%29%5E2-9%2B4=0
%28y+-+3%29%5E2+-+5+=+0
%28y+-+3%29%5E2+=+5+
%28y+-+3%29+=+sqrt%285+%29
solutions:
y=3%2Bsqrt%285+%29 or y=3-sqrt%285+%29+

now find x
x+=+6+-y=>x+=+6+-%283%2Bsqrt%285+%29%29=6-3-sqrt%285+%29=>x=3-sqrt%285+%29
or
x+=+6+-y=>x+=+6+-%283-sqrt%285+%29%29=6-3%2Bsqrt%285+%29=>x=3%2Bsqrt%285+%29

so, (x,y) pairs are:
(3%2Bsqrt%285+%29,3-sqrt%285+%29)
and
(3-sqrt%285+%29,3%2Bsqrt%285+%29)