Question 1088213
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<pre>
(1)    {{{(x+1)^2+2(y-4)^2}}} = 12 
(2)    {{{y^2-8y}}} = 4x-16


(1)    {{{x^2 + 2x + 1 + 2*(y^2-8y+ 16)}}} = 12


From (2), substitute and replace (y2 - 8y) by 4x-16. You will 

      {{{x^2 + 2x + 1 + 2*(4x-16+ 16)}}} = 12.

Simplify

     {{{x^2 + 2x + 1 + 8x}}} = 12,

     {{{x^2 + 10x - 11}}} = 0.

Factor left side and get

     (x+11)*(x-1) = 0.

The roots are x = -11 and x = 1.


From this point, complete the assignment on your own.
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Solved.


For similar prototypes/samples see the lesson

&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, 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 lesson is the part of this online textbook under the topic 
"<U>Systems of equations that are not linear</U>".