Solving a three variable equation I have three given values, suppose a=1.86, b=2.6 and c=4.2. Now I have to figure out x,y,z such that 


*

*$x\gt 0,y\gt 0$ and $z\gt 0$   

*$x+y+z=1$  

*$a*x\gt 1, b*y\gt 1$ and $cz\gt 1$  
I need a generalized solution steps for this to implement in programming.
Thanks.

$\left\{ {\begin{array}{*{20}{l}}
{x > \frac{1}{a} \Rightarrow x = \frac{1}{a} + X}\\
{y > \frac{1}{b} \Rightarrow y = \frac{1}{b} + Y}\\
{z > \frac{1}{c} \Rightarrow z = \frac{1}{c} + Z}
\end{array}} \right.$  where $0 < X,Y,Z$
$   \Rightarrow \frac{1}{a} + X + \frac{1}{b} + Y + \frac{1}{c} + Z = 1 \Rightarrow X + Y + Z = 1 - \frac{1}{a} - \frac{1}{b} - \frac{1}{c}$ $\hspace{.3cm}$(*)
(*) is an equation of surface where cut each axis in $1 - \frac{1}{a} - \frac{1}{b} - \frac{1}{c}$. 
Your solution is all the point on this surface which that lie on the first quadrant.
