$\left \{ {{x²+y²=1} \atop {-x²-5xy+2y²=3}} \right.$

\begin{cases} x^2+y^2=1\\-x^2+5xy+2y^2=3 \end{cases}

`⇔-x^2+5xy+2y^2=3x^2+3y^2`

`⇔4x^2-5xy+y^2=0`

`⇔(x-y)(4x-y)=0`

`⇔`\(\left[ \begin{array}{l}x-y=0\\4x-y=0\end{array} \right.\) 

`⇔`\(\left[ \begin{array}{l}x=y\\4x=y\end{array} \right.\) 

`⇔`\(\left[ \begin{array}{l}2x^2=1\\17x^2=1\end{array} \right.\) 

`⇔`\(\left[ \begin{array}{l}x=1/(±√2)\\x=1/(±√17)\end{array} \right.\)