Solve the system by the substitution method.

xy=9

x^2+y^2=82

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