<PRE><B>Question 1099296</B>
.
First of all, &amp;nbsp;by substituting your &amp;nbsp;&quot;solutions&quot; &amp;nbsp;directly into the given equations &amp;nbsp;(&quot;the &quot;CHECKING&quot; step) 


you can see that &amp;nbsp;(0,2) &amp;nbsp;&lt;U&gt;IS NOT THE SOLUTION&lt;/U&gt;, &amp;nbsp;while (6/5,8/5) &amp;nbsp;&lt;U&gt;IS&lt;/U&gt;.



&lt;pre&gt;
Let solve this system together:

{{{x^2 + y^2}}} = 4,     (1)
3x - y = 2.     (2)


From (2), express y = 3x-2. Next, substitute it into equation (1), replacing &quot;y&quot;. You will get 

{{{x^2 + (3x-2)^2}}} = 4.


Simplify it step by step:

{{{x^2 + 9x^2 - 12x + 4}}} = 4  ====&gt;  {{{10x^2 - 12x}}} = 0  ====&gt;  (factoring left side)  ====&gt;

2x*(5x-6) = 0.


The solutions for x are  0  and   x= {{{6/5}}}.


a)  If  x= 0,  then  from (2)  y = 3x-2 = 3*0-2 = -2.

    So, the pair  (x,y) = (0,-2)  is one solution.


b)  If x= {{{6/5}}},  then  y = 3x-2 = {{{3*(6/5)-2}}} = {{{18/5 - 10/5}}} = {{{8/5}}}.

     So, the pair  (x,y) = (6/5,8/5) is the other solution.


&lt;U&gt;Answer&lt;/U&gt;.  The solutions are  (0,-2)  and  (6/5,8/5).
&lt;/pre&gt;

You can &lt;U&gt;CHECK&lt;/U&gt;  that these pairs satisfy both original equations.


---------------
To see more solved problems for systems of equations of this type, look into the lessons

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-alg-eqns-of-deg2-deg1.lesson&gt;Solving the system of algebraic equations of degree 2 and degree 1&lt;/A&gt;, 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-algebraic-equations-of-degree-2.lesson&gt;Solving the system of algebraic equations of degree 2&lt;/A&gt;, 

in this site.


Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-I - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lessons are the part of this online textbook under the topic &quot;&lt;U&gt;Systems of equations that are not linear&lt;/U&gt;&quot;.



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.



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