SOLUTION: can you help me solve this system of equations 2x+3y=2 2x^2+xy+y^2=8 thank you

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Question 224925: can you help me solve this system of equations
2x+3y=2
2x^2+xy+y^2=8
thank you

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!



The graph of this is a line intersecting a slanted ellipse.
You don't have to draw the graph, but I thought I'd graph
it for you so you'd know to expect two solutions:



It looks as though one solution (where the line intersects
the ellipse is about (-2,2) and the other one looks about 
(2.1,-.8) or so.

Solve the first equation for x





Substitute in the second equation














Multiply through by 2 to clear of fractions:



















                  
                    
                         

               
             
                
                 
                  
                          
                         
                          

So the two solutions are:

 and 

Edwin

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