# Finding positive solutions to two equations

After solving a system of equations I get this:

x + 0.03125z = 0.242813
y + 0.40625z = 0.456563


How can I filter solutions that are only positive for x y and z

Ted

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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.

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Perhaps you could glean something from this.

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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 is positive.

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.

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