SOLUTION: Solve each system of equations: {3x^2+4xy+5y^2=8 and x^2+3xy+2y^2=0 When I try to solve it, it turns out to be really messy. PLease use elimination or substituion in your answe

Question 1021116: Solve each system of equations:
{3x^2+4xy+5y^2=8 and x^2+3xy+2y^2=0
When I try to solve it, it turns out to be really messy. PLease use elimination or substituion in your answer. Thank you
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(Equation A)
(Equation B)
The key lies in factoring Eqn. B: <==> (x+y)(x+2y) = 0.
We discuss 2 cases:
(i) When x+y = 0, or y = -x. Substitute this into Eqn.A
==> ==> ==>
==> or
==> the solutions (, ) and (, ).
(ii) The case of x+2y = 0, or x = -2y, is handled in a similar manner.
After doing so we get the pair of solutions (, ) and (, ).
Therefore the solutions are (, ), (, ), (, ), and (, ).

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