xy=a\left(x+y\right)-c,\:xz=a\left(x+z\right)-c,\:yz=a\left(y+z\right)-c,\:xy+zy+xz\:=50,\:\left(\lfloor x\rfloor -x\right)+\left(\lfloor y\rfloor -y\right)+\left(\lfloor z\rfloor -z\right)=0
You asked:
Solve the system of equations:\[\begin{aligned}x y &= a\left( x + y \right) - c\\x z &= a\left( x + z \right) - c\\y z &= a\left( y + z \right) - c\\x y + z y + x z &= 50\\\left\lfloor x \right\rfloor - x + \left\lfloor y \right\rfloor - y + \left\lfloor z \right\rfloor - z &= 0\end{aligned}\]