$$\frac{\lvert a \rvert}{2d} +\frac{\lvert b \rvert}{3e} +\frac{\lvert c \rvert}{4f}$$

Algebra Level 1

If the following holds for any numbers $$x$$ and $$y$$, what is the value of $$\frac{\lvert a \rvert}{2d} +\frac{\lvert b \rvert}{3e} +\frac{\lvert c \rvert}{4f}$$: $4x+9y+16=a^2 x+b^2 y+c^2=\frac{x}{d}+\frac{y}{e}+\frac{1}{f}?$

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