SOLUTION: find all solutions of the system of equations. {x + sqrt (y) = 0 {y^2 - 2x^2 = 3

Algebra ->  Matrices-and-determiminant -> SOLUTION: find all solutions of the system of equations. {x + sqrt (y) = 0 {y^2 - 2x^2 = 3      Log On


   

Question 473872: find all solutions of the system of equations.
{x + sqrt (y) = 0
{y^2 - 2x^2 = 3
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+-sqrt%28y%29
Substitute into the bottom equation:
y%5E2+-+2y+=+3, or y%5E2+-+2y+-+3+=+0
<==> (y - 3)(y + 1) = 0 ==> y = 3, -1
eliminate y = -1 (Why?)
==> x+=+-sqrt%283%29
The solution point is thus (-sqrt%283%29, 3)