xy=9 and
x^2+y^2=82
we manipulate the first equation to get
xy=9
divide both sides by x
y=9/x
subtitute y=9/x into x^2+y^2=82
x^2+(9/x)^2=82
x^2+81/x^2=82
multiply both sides by x^2 to get rid of the denomator (bottom number)
x^4+81=82
subtract 81 from both sides
x^4=1
find the fourth root of 1 and get
x=1
subtitute into origoal equation xy=9 and get
(1)y=9
y=9