how do you solve following system of non linear equations

Question : Solve following system of non linear equations \[x=y\left(1-\left(x^2+y^2\right)\right) , y=x\left(1-\left(x_2+y^2\right)\right) \]Solution : \[x=y\left(1-\left(x^2+y^2\right)\right) \] (1) \[y=x\left(1-\left(x_2+y^2\right)\right) \] (2) From eqn (1) \[\frac{x}{y}=1-\left(x^2+y^2\right)\] From eqn (2) \[\frac{y}{x}=1-\left(x^2+y^2\right)\] Equating these equations \[\frac{x}{y}=\frac{y}{x}\] \[x^2-y^2=0\] x=y, x=-y Substituting x=y into eqn (1)…

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