Linear Manipulating

Algebra Level 3

Given that a,ba,b and cc are non-zero numbers that satisfy the system of equations below.

{a10b=0c+b=210acc=20 \begin{cases} a-10b = 0 \\ c+b=2 \\ 10ac- c = 20 \\ \end{cases}

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

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