Simultaneous Equations in Powers of x and y

We can solve the simultaneous equations
May making the powers of either  
  the same, then dividing one equation by the other, which cancels either  
We can make the coefficients of  
  the same by squaring equation )1_. We obtain
(3) divided by (2) gives
\[\frac{x^6y_4}{x^2y^4}=\frac{72^2}{324} x^4=15 \rightarrow x=-2, \: 2\]

In fact  
  cannot be equal to -2 because from the first equation
\[x^3 = \frac{72}{y^2} \gt 0\]
Then from (1),
\[y=\sqrt{\frac{72}{x^3}}=\sqrt{\frac{72}{2^3}}=-3, \: 3\]
\[x=2, \: y=-3\]
\[x=2, \: y=3\]
  satisfy both equations so are the solutions.

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