Algebra · Systems of equations · Rational equations · Factorisation · Quartic equations · Domain restrictions
Find all pairs of real numbers \(x\) and \(y\) that satisfy the system
\[ \frac{y^{3} + 15x^{2}}{y^{4} - x^{3}} = \frac{y^{2} + 15x}{y^{3} - x^{2}} , \]
\[ \frac{1500y^{3} + 4x^{2}}{9y^{4} - 4} = \frac{1500y^{2} + 4x}{9y^{3} - 4} . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2019, 1. letnik, category A, problem B3 (printed as B2; the problems PDF misprints the label). Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source