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Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

Solve the system of equations algebraically for $(x, y)$ : $x + y = 42$ , $x - y = 10$ .

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