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

Answered by apologiabiology | 2024-06-10

To solve the system x y = 9 and x 2 + y 2 = 82 using substitution, we express one variable in terms of the other and substitute it into the second equation. This leads us to a polynomial equation that we can factor and solve for both variables. The solutions are ( 9 , 1 ) , ( − 9 , − 1 ) , ( 1 , 9 ) , and ( − 1 , − 9 ) .
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Answered by apologiabiology | 2024-10-07