a*x^(a-1)*y^b+z=0
b*x^(a)*y^(b-1)+z=0
x+y+1=0
solve for x and y

Question

a*x^(a-1)*y^b+z=0
 b*x^(a)*y^(b-1)+z=0 
x+y+1=0
solve for x and y

anonymous · Answer

Maybe you should write out the whole equation and not in this form... It's too messy...

anonymous · Answer

$$a x^{a-1}y ^{b}+\lambda=0$$
$$bx ^{a}y ^{b-1}+\lambda=0$$
x+y-1=0

anonymous · Answer

$$
\left\{
\begin{array}{l}
ax^{a-1}y^b+z=0\
bx^ay^{b-1}+z=0\
x+y+1=0
\end{array}\right.
$$

anonymous · Answer

Now is it x+y+1 or x+y-1 ?

anonymous · Answer

$$
\left\{
\begin{array}{l}
ax^{a-1}y^b+z=0\
bx^ay^{b-1}+z=0\
x+y-1=0
\end{array}\right.
$$
Plug the second equation into the first
and you get
$$ x^{a-1}y^{b-1}(ay-bx) = 0 $$
If $$a>1$$ then x=0 and y=1 is a solution.
If $$b>1$$ then x=1 and x=0 is a solution.
If $$a+b\not=0$$ then you may infer by plugging
the above equation into the third one that
$$ x=\frac{a}{a+b}, y=\frac{b}{a+b} $$.