I've three equations and want to calculate the values of the three variables $x$, $y$ and $z$. The problem is, that $x$ and $y$ are raised to decimal power and I don't know how to deal with them.
The equations are:
$I: 8x^{-0.6}y^{0.6}-8z=0$
$II: 12x^{0.4}y^{-0.4}-3z=0$
$III: -8x-3y+10000=0$
I've multiplied the first equation with $3$, the second one with $-8$ and formed the third equation to get $x$ alone on one side. When I put it all together I get: $\frac{24y^{0.6}}{(\frac{10000-3y}{8})^{0.6}}-\frac{96(\frac{10000-3y}{8})^{0.4}}{y^{0.4}}=0$
When I use a tool to calculate it, I get $y=2000$ as a result, but I don't know how to get to this by hand. Can anyone tell me how to get rid of the decimal exponent of $x$ and $y$? Is there maybe an easier way to solve this equation system?
Eliminating $z$ from the first two equations, you should get $$\frac{24 y^{0.6}}{x^{0.6}} = \frac{96 x^{0.4}}{y^{0.4}} $$ and clearing out the denominators and dividing by $24$ should give you $$ y = 4 x $$ Now plug that in to the third equation, and solve.