Simultaneous Quadratic Equations

Solve the system of equations for $x$ and $y$ : $x^{2} + y^{2} - 3 = 3 x y$ and $2 x^{2} - 6 + y^{2} = 0$ .

~15 minAnswer checked instantlysystems of equationsquadratic systemsradicals

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.b, No. 12

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).