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Found problems: 1

2008 Harvard-MIT Mathematics Tournament, 29
Tags: geometry , matrix , rotation , linear algebra , rotation matrix , geometric transformation
Let $ (x,y)$ be a pair of real numbers satisfying \[ 56x \plus{} 33y \equal{} \frac{\minus{}y}{x^2\plus{}y^2}, \qquad \text{and} \qquad 33x\minus{}56y \equal{} \frac{x}{x^2\plus{}y^2}. \]Determine the value of $ |x| \plus{} |y|$.