SOLUTION: x2−2y=11 3x2+y2=24 I'm suppose to solve the system of equations and need, if I should use elimination or plug in and my teacher said there should be a total of four solution

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: x2−2y=11 3x2+y2=24 I'm suppose to solve the system of equations and need, if I should use elimination or plug in and my teacher said there should be a total of four solution      Log On


   

Question 852363: x2−2y=11
3x2+y2=24 I'm suppose to solve the system of equations and need, if I should use elimination or plug in and my teacher said there should be a total of four solutions
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You must want these equations as given ones:
x%5E2-2y=11 and 3x%5E2%2By%5E2=24.
-------- A parabola intersecting a circle. Yes, MAYBE four solutions for that system; depends....

What method to solve the system, depends on what you know and what you want to use (unless you are directed to use a particular method). That choice appears to be YOURS.

To not remove the opportunity for you to begin to solve the system, I will begin a couple of steps off the site page and continue some of it on the site page...
A possible equation resulting from a solution process can be highlight_green%28y%5E2-6y%2B9=0%29. This is a quadratic equation in y, and it is factorable.

Continuing with that factorization,
%28y-3%29%5E2=0
highlight%28y=3%29 and this will mean through x%5E2=11-2y, that highlight%28x=-sqrt%285%29%29 or highlight%28x=sqrt%285%29%29.
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LOOKS LIKE TWO SOLUTIONS, NOT FOUR SOLUTIONS.


One reason the circle appears split is because the circle is made of two functions put together on the same graph.
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This graph very obviously shows two points of intersection; NOT four.