SOLUTION: Hi, please help me solve this by using the addition method. Thank you so much! {{{ x^2+y^2=16 }}} {{{ 4x^2+9y^2=36 }}}

Their graphs are a circle with an ellipse inside, like this
 

They do not intersect so there are no real solutions.  However 
there are imaginary solutions:

Multiply the first equation through by -4



Now add them term by term



      

      

      

      

      

      

       

           

      

When the first unknown you find is complicated, do not substitute
to find the other unknown.  Instead, start over and eliminate the
other unknown:



Multiply the first equation through by -9



Now add them term by term



      

      

      

      

      

      

       

           

       

So there are 4 solutions:



Edwin