SOLUTION: what are the solutions to the nonlinear system of equations below? check all that apply x^2+y^2=9 x^2/3^2-y^2/3^2=1 A. (3, 3) B. (-3, -3) C. (3, 0) D. (0, 3) E. (0, -

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: what are the solutions to the nonlinear system of equations below? check all that apply x^2+y^2=9 x^2/3^2-y^2/3^2=1 A. (3, 3) B. (-3, -3) C. (3, 0) D. (0, 3) E. (0, -      Log On


   

Question 878504: what are the solutions to the nonlinear system of equations below?
check all that apply
x^2+y^2=9
x^2/3^2-y^2/3^2=1
A. (3, 3)
B. (-3, -3)
C. (3, 0)
D. (0, 3)
E. (0, -3)
F. (-3, 0)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A good method is solve one equation either for x%5E2 or for y%5E2, and substitute into the other equation, and solve for this single variable. Return to the first variable and solve.

y%5E2=9-x%5E2.
Now substitute ...
x%5E2%2F9-%289-x%5E2%29%2F9=1
x%5E2-%289-x%5E2%29=9
2x%5E2-9=9
2x%5E2=9%2B9=18
x%5E2=9
x=-3 OR x=3.

Resuming with y%5E2=9-x%5E2, either x solution will give the same y.
y%5E2=9-9
y%5E2=0
y=0

SOLUTIONS: (-3,0) and (3,0).