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UKMT Maclaurin Olympiad, 2016

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

What are the solutions of the simultaneous equations: $3x^2 + xy - 2y^2 = -5$ ; $x^2 + 2xy + y^2 = 1$ ?

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.