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I want to solve the system of equations

(y + 1)(a - x^p*y^q) == 0
(y + 1)x^p*y^q - c*y == 0

But I am getting the massage

this system can't be solved by known methods

Can anyone help me?

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    $\begingroup$ Yeah, post the code you are using and we will help you. $\endgroup$ – Sektor Jul 22 '16 at 7:28
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Introduce a new variable $z=x^py^q$.

eqs1 = {(y + 1) (a - z) == 0, (y + 1) z - c == 0}
res1 = Solve[eqs1, {y, z}]
eq2 = (z == x^p y^q /. First[res1])
Solve[eq2, x]

The answer is $y=\frac{c-a}{a}$ and $x=\left(a \left(\frac{c-a}{a}\right)^{-q}\right)^{1/p}$.

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  • $\begingroup$ I get a different solution: sys /. {y -> -a/(a - c), x -> (a (-a/(a - c))^-q)^(1/p)} // Simplify[#, {p, q} \[Element] Integers] &, with sys being the OP's system. $\endgroup$ – Michael E2 Jul 23 '16 at 5:05
  • $\begingroup$ Thank for the answer by yarchik and Mr. Wizard. The second equation in eqs1 should be (y+1)z-c y==0. It is corrected by Michael. $\endgroup$ – Savata Jul 23 '16 at 6:31

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