Algebra · Systems of equations · Factorisation · Difference of squares · Case analysis
Find all pairs of real numbers \(x\) and \(y\) satisfying
\[ x + y^{2} = xy + 1 \qquad\text{and}\qquad xy = 4 + y . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2011, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source