Question 1095507
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<pre>
1.  First, you can easily check your solution.

    {{{(1+sqrt(5))^2}}} + {{{(-1+sqrt(5))^2}}} = 

    {{{1 + 2*sqrt(5) + 5}}} + {{{1 - 2*sqrt(5) + 5}}} = 1 + 1 + 5 + 5 = 12.


        Is it equal to 8 ? - NO.  
    
        What does it mean ?  - It means that your solution is incorrect.



2.  Very straightforward way is THIS: From the second equation express x = 2 + y

    and substitute it into first equation.  You will get

    {{{(2 + y)^2}}} + {{{y^2}}} = 8.

    It is your quadratic equation for single unknown "y".

    Simplify and solve it.
</pre>


To see many other similar solved problems (your samples), look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-alg-eqns-of-deg2-deg1.lesson>Solving the system of algebraic equations of degree 2 and degree 1</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-algebraic-equations-of-degree-2.lesson>Solving the system of algebraic equations of degree 2</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Systems of equations that are not linear</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.