SOLUTION: xy=4 x^2+y^2=8 How do I solve this system by the substitution method?

Algebra ->  Equations -> SOLUTION: xy=4 x^2+y^2=8 How do I solve this system by the substitution method?      Log On


   

Question 958358: xy=4
x^2+y^2=8
How do I solve this system by the substitution method?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

xy=4...........(1)
x%5E2%2By%5E2=8.......(2)
--------------------
xy=4...........(1)...solve for x
x=4%2Fy..........substitute in (2)
%284%2Fy%29%5E2%2By%5E2=8.......(2) solve for y
16%2Fy%5E2%2By%5E2=8
%2816%2By%5E4%29%2Fy%5E2=8
16%2By%5E4=8y%5E2
y%5E4-8y%5E2%2B16=0
%28y%5E2%29%5E2-8y%5E2%2B4%5E2=0
%28y%5E2-4%29%5E2=0
%28y%5E2-4%29%28y%5E2-4%29=0
%28y-2%29%28y%2B2%29%28y-2%29%28y%2B2%29=0
solutions: two double solutions
if %28y-2%29=0=>y=2
if %28y%2B2%29=0=>y=-2
now find x
x=4%2Fy substitute =>y=2
x=4%2F2
x=2
and
x=4%2Fy substitute =>y=-2
x=4%2F-2
x=-2
so,
x=2,y=2
or
x=-2,y=-2