Suppose \( p, q, r \neq 0 \) and the system of equations \( (p+a) x+b y+c z=0, \quad a x+(q+b) y...

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Suppose \( p, q, r \neq 0 \) and the system of equations \( (p+a) x+b y+c z=0, \quad a x+(q+b) y+c z=0 \) \( a x+b y+(r+c) z=0 \)
has a non-trivial solution, then the value of \( \frac{p}{a}+\frac{q}{b}+\frac{r}{c} \), is
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