Question 1106112
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Please accept these my notices:


1.    From  https://english.stackexchange.com/questions/3640/is-substract-versus-subtract-a-proper-word


<pre>
    "Subtract" is the word. Though the obsolete word "substract" did exist, any occurrence you see these days 
     is most likely just a common mistake, formed by analogy either with "abstract" or with other languages 
     whose corresponding words do have two 's's. Many recent dictionaries do not list "substract".
</pre>


2.  &nbsp;&nbsp;Even if to treat your  &nbsp;"substraction" &nbsp;as &nbsp;<U>subtraction</U>, &nbsp;<U>it DOES NOT work</U>&nbsp; for this system.



3.  &nbsp;&nbsp;Instead, &nbsp;the &nbsp;<U>SUBSTITUTION</U> &nbsp;method works:


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;From the linear equation express  &nbsp;x = -2y  &nbsp;and substitute it into the non-linear equation. &nbsp;You will get


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(-2y-1)^ + (y-1)^2 = 5.


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is the quadratic equation. &nbsp;Simplify it to the standard form and solve by any method.



================
So, the final conclusion is that the condition in this post is <U>INCORRECT</U>.


The correct condition is <U>THIS</U>:


<pre>
    solve nonlinear equation by using the SUBSTITUTION method.
    1) {x+2y=0 (x-1)^2 + (y-1)^2=5
</pre>


And I just showed you how to solve it . . . 



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See the lesson

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

in this site.


You will find there many similar solved systems.