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x +(3x-y)/(x^2 + y^2) = 3, y - (x + 3y/(x^2 + y^2) = 0

Source: 15th -a QEDMO problem 7 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

May 29, 2021

algebrasystem of equationsSystem

Problem Statement

Find all real solutions

x, y

of the system of equations

\begin{cases} x + \dfrac{3x-y}{x^2 + y^2} = 3 \\ \\ y-\dfrac{x + 3y}{x^2 + y^2} = 0 \end{cases}