Linear Manipulating

Algebra Level 3

Given that \(a,b\) and \(c\) are non-zero numbers that satisfy the system of equations below.

\[ \begin{cases} a-10b = 0 \\ c+b=2 \\ 10ac- c = 20 \\ \end{cases} \]

Find the value of \( \dfrac 1a + \dfrac 1b + \dfrac 1c \).

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