$(5$ points$)$ Solve the following system for $x,y,z.$ Please show you work in detail.

$\frac{1}{x}\frac{2}{y}-\frac{4}{z}=1$

$\frac{2}{x}\frac{3}{y}\frac{8}{z}=0$

$-\frac{1}{x}\frac{9}{y}\frac{10}{z}=5$