What are the solutions to the nonlinear system of equations below? Check all that apply. x² + y² = 9 {x}^(2) \frac{ {3}^(2) } - {y}^(2) \frac{ {3}^(2) } = 1 ​

Question

What are the solutions to the nonlinear system of equations below?

Check all that apply.
x² + y² = 9

`{x}^(2) \frac{ {3}^(2) } - {y}^(2) \frac{ {3}^(2) } = 1`
​

Answer 1

B, E

Explanation:

`x^(2) +y^(2)=9`

`(x^(2) )/(3^(2)) - (y^(2) )/(3^(2)) =1`

`x^(2) =9-y^(2) \\(x^(2) )/(3^(2)) - (y^(2) )/(3^(2)) =1`

`x^(2) =9-y^(2)`

`(9-y^(2) )/(3^(2) ) -(y^(2) )/(3^(2) )=1`

`x^(2) =9-y^(2)`

`(1)/(9) * (9-y^(2) )-(y^(2) )/(9) = 1`

`x^(2) =9-y^(2)`

`1-(2y^(2) )/(9) =1`

`x^(2) =9-y^(2)`

`-(2y^(2) )/(9) =0`

`x^(2) =9-y^(2)`

`y^(2) =0`

`x^(2) =9-y^(2)\\y=0`

`x^(2) =9\\y=0`

`x=3 \\y=0\\\\or\\\\x=-3\\y=0`