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If $a$, $b$ and $c$ are numbers such that
$$-3b + 7c = -10$$
$$b - 2c = 3$$
$$a + 2b - 5c = 13$$
what is the value of $a$?

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.