System
Source: HMMT 2008 Guts Problem 29
May 13, 2008
geometrygeometric transformationrotationLaTeXlinear algebramatrixrotation matrix
Problem Statement
Let 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|.