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2015-08-20T18:40:07+05:30

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1)  a x + b y = a²
2)  b x + a y = b²

   (1) * b - (2) * a =>    (b² - a²) y = ab (a - b)

  either a = b,  or
        y = - a b / (a + b)        then b x = b² + a² b / (a+b)
   =>       x =  (a² + ab + b²) / (a + b)  ,   if a+ b ≠ 0

If  a  = b,  then x + y = a   ie.,  x = a - y    this has infinite number of solutions.
Otherwise, there is one solution,   and  a + b ≠ 0.
 
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it has infinite number of solutions
if a = b then there are infinite solutions. If a ≠ b and a ≠ -b then, there is one solution only.