Let p, q, r be non-zero real numbers that are, respectively, the $10^{\text {th }}, 100^{\text {th }}$ and $1000^{\text {th }}$ terms of a harmonic progression. Consider the system of linear equations $$ \begin{aligned} & x+y+z=1 \\ & 10 x+100 y+1000 z=0 \\ & q r x+p r y+p q z=0 \end{aligned} $$