# How can I solve this system?

Really hard problem!!

\begin{align} xy&=-2 \\ xy^{a-1} &=-512 \\ x(y^a-1 ) &= 341y-341 \end{align}

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Plugging the 1st and 2nd equations into the 3rd, we get a quadratic equation for y. – pharmine Nov 9 '11 at 9:42
Did you want the third equation to be $x(y^a-1)=-341y-341$? The solution is much nicer then. – David Mitra Nov 9 '11 at 10:05

From the first two (divide them) you get $y^{a-2}=256$.
So the third becomes $xy\cdot y \cdot 256 -x=341y-341$.
$-512 y-x=341y-341$. Plug $x=-2/y$ in this last equation you get a quadratic equation.