# How can I solve my system of simultaneous polynomial equations?

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?

• Yeah, post the code you are using and we will help you. – Sektor Jul 22 '16 at 7:28

Introduce a new variable $z=x^py^q$.
eqs1 = {(y + 1) (a - z) == 0, (y + 1) z - c == 0}

The answer is $y=\frac{c-a}{a}$ and $x=\left(a \left(\frac{c-a}{a}\right)^{-q}\right)^{1/p}$.
• 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. – Michael E2 Jul 23 '16 at 5:05