\[x^3y_2=72\]
(1)\[x^2y^4=324\]
(2)May making the powers of either
\[x\]
or \[y\]
the same, then dividing one equation by the other, which cancels either \[x\]
or \[y\]
.We can make the coefficients of
\[y\]
the same by squaring equation )1_. We obtain
\[x^6y_4=72\]
(3)(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
\[x\]
cannot be equal to -2 because from the first equation \[x^3 = \frac{72}{y^2} \gt 0\]
.Then from (1),
\[y=\sqrt{\frac{72}{x^3}}=\sqrt{\frac{72}{2^3}}=-3, \: 3\]
.\[x=2, \: y=-3\]
and \[x=2, \: y=3\]
satisfy both equations so are the solutions.