Jumbling Mumbling!

$x-y=0$

$\Rightarrow x=0+y$

$\Rightarrow x=y$

$\therefore$ We get $x=y$

Since $\log_0 a^b = -\infty$ , we can say from the fourth equation $x = 0$

Since $x=y$ , $y = 0$

Substituting the values in the second equation, we get: $\frac{0+0}{z}\times10^{-15}+z=\frac{z}{0}$ $\Rightarrow 0\times10^{-15}+z=0$ $\Rightarrow 0+z=0$ $\Rightarrow z=0$ Therefore, since $x=y=z=0$ ; $x+y+z= \boxed{0}$