Rewrite the left side of the first equation as :



Use FOIL:



Combine middle terms, which are like terms:



So now the system is:

 

Multiply the second equation through by 



Add the left and right sides of the system:



Solve for  by dividing both sides by :



Simplifying:



Substituting  for q in









Multiply through every term by 



Get 0 on the right by adding 
to both sides:



The left side factors as



Setting each factor = 0:



=±



=±
=±
=±
=±

So the four values for  are

, , , 

We must now find a value of q to go with
each of these.  So we use



Substituting  



Rationalize the denominator by multiplying top and
bottom by 







So one solution is (p,q) = (,)

--------------------------

Substituting  



Rationalize the denominator by multiplying top and
bottom by 







So a second solution is (p,q) = (,)

-------------------------

Substituting  





Rationalize the denominator by multiplying top and
bottom by 







So a third solution is (p,q) = (,)

--------------------

Substituting  





Rationalize the denominator by multiplying top and
bottom by 







So the fourth solution is (p,q) = (,)

Edwin