SOLUTION: Identify the solutions to the system of equations: x2 + y2 = 25 16x2 + 25y2 = 400

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: Identify the solutions to the system of equations: x2 + y2 = 25 16x2 + 25y2 = 400       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 43748: Identify the solutions to the system of equations:
x2 + y2 = 25
16x2 + 25y2 = 400

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 = 25
y^2 = 25 - x^2
so:
16x^2 + 25y^2 = 400
16x^2 + 25(25 - x^2) = 400
16x^2 + 625 - 25x^2 = 400
-9x^2 = -225
x^2 = 25
x = +-5
Plug:
x^2 + y^2 = 25 and x^2 + y^2 = 25
5^2 + y^2 = 25 and (-5)^2 + y^2 = 25
y^2 = 0 and y^2 = 0
y = 0 and y = 0
(5,0) and (-5,0)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28-x%5E2+%2B+25%29%2C+-sqrt%28-x%5E2+%2B+25%29%2C+sqrt%28%28-16%2F25%29x%5E2+%2B+16%29%2C+-sqrt%28%28-16%2F25%29x%5E2+%2B+16%29+%29+