Finding positive solutions to two equations After solving a system of equations I get this:
\begin{cases} x + 0.03125z = 0.242813 \\ y + 0.40625z = 0.456563\end{cases}
How can I filter solutions that are only positive for $x$, $y$ and $z$
Ted
 A: Perhaps you could glean something from this.
A: Are your constants really reals?  It looks like it may be rounded from $x+\frac{z}{32}=\frac{777y}{3200}+\frac{13z}{32}=\frac{1461}{3200}$  If not, you can use the decimals in the following.  Break it into $3200x+100z=1461$ and $777y+1300z=1461$.  You can see that $x \le \frac {1461}{3200}, y \le \frac {1461}{777}, z\le \frac {1461}{1300}$ and as any one gets larger, it drives down the others.
A: For equations that look complicated, it helps to artificially simplify them by guessing really boring values that you might solve for. 
For example let $y$ and $z$ be $0$ (yes, that's not positive but it's not particularly negative either (unless you're speaking French)..actually just consider $x,y,z$ as non-negative...makes things easier all around). At least $y$ and $z$ are as small as possible. Then you'll notice that $x$ is as big as your RHS (right hand side), which really means it is as big as possible. And notice that $x>0$.
Now do the same for $y$ (set $x$ and $z$ to $0$) and separately for $z$ (set $x$ and $y$ to $0$). 
Notice now that if you subtract a little from any one of them, you'll be able to add a little more to the others (not the same amount for each). 
So the smallest value for each could be $0$, and the largest value will be what your solutions are for the above simplifications. And by the above 'notice', all values in between will work.
