Out of the following options, which is a solution to:
and
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Taking x 2 = y 3 ⇒ y = x 3 2 , substituting this value into other equation will yield:
x y = y x ⇒ x x 3 2 = ( x 3 2 ) x ;
or x 3 2 = 3 2 x ⇒ x 2 = 2 7 8 x 3 ;
or 8 x 3 − 2 7 x 2 = 0 ⇒ x 2 ( 8 x − 2 7 ) = 0 ⇒ x = 0 , 8 2 7 and y = 0 , ( 8 2 7 ) 3 2 = 4 9 .
Hence the solutions are ( x , y ) = ( 0 , 0 ) ; ( 8 2 7 , 4 9 ) . But 0 0 is indeterminate, which only leaves x = 8 2 7 , y = 4 9 .