SOLUTION: Use any method to solve the nonlinear system. (Order your answers from smallest to largest x, then from smallest to largest y. If there is no solution, enter NO SOLUTION.) x^2

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Question 1129186: Use any method to solve the nonlinear system. (Order your answers from smallest to largest x, then from smallest to largest y. If there is no solution, enter NO SOLUTION.)
x^2 + y^2= 6
xy= 1
Can someone help, I use the method of and my final answers, which keeps being tagged incorrect, have been:
x: -1, y: +1
x: - +1, y: - -1
x: +1, y: -1
x: - -1, y: - +1
Am I just incorrectly ordering them from smallest to least or are the entire answers wrong?
Here is some of my work:
For x^2 + y^2= 6, substitute x with 1/y.
(1/y)^2 +y^2= 6;
For xy=1, substitute y with +1
x( +1 )=1
x= -1
For xy=1, substitute y with -1
x( -1 )=1
x= +1
For xy=1, substitute y with - +1
x(- +1 )=1
x= - -1



Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

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,


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.
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Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

........eq.1
........eq.2
-----------------------
........eq.2=>
substitute in eq.1

........eq.1
...multiply by

...factor


solutions: there will be four

if




...simplify


so, or


if






or



now find using all 4 solutions for

if , since we have




if



if




if






Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
Your solutions are correct. I mean, you have the set of four solutions correctly.


Their ordering instruction is presented in a very strange way.


You can order the pairs looking in x first, but then you have no choice to order in y.


It forces me to think that they ask you to make your ordering TWICE:


    - first time by ordering 4 pairs looking in x;  

    - and the second time by ordering the same 4 pairs looking in y.

In any way, it is not a Mathematical way to formulate an assignment.

----------------

The two other tutors presented the solutions to the roots, although nobody asked them to do it - you just have the solutions correctly.


The post by @josgarithmetic is the way to NOWHERE, as it often happens with him - so you can simply IGNORE his post, for your safety.



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