[latex] \left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {5x^{2}+9xy-2y^{2}=0}} \right. [/latex]Решите систему уравнений

[latex] \left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {5x^{2}+9xy-2y^{2}=0}} \right. \\\ \left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {5x^{2}+10xy-xy-2y^{2}=0}} \right. \\\ \left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {5x(x+2y)-y(x+2y)=0}} \right. \\\ \left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {(x+2y)(5x-y)=0}} \right. [/latex] [latex] \left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {x+2y=0}} \right. \\\ x=-2y \\\ 3(-2y)^2+5(-2y)y-4y^2=-2 \\\ 12y^2-10y^2-4y^2=-2 \\\ y^2=1 \\\ y_1=1 \\\ y_2=-1 \\\ x_1=-2 \\\ x_2=2[/latex] [latex]\left \{ {{3x^{2}+5xy-4y^{2}=-2} \atop {5x-y=0}} \right. \\\ y=5x \\\ 3x^2+5x(5x)-4(5x)^2=-2 \\\ 3x^2+25x^2-100x^2=-2 \\\ x^2= \frac{1}{36} \\\ x_3= \frac{1}{6} \\\ x_4=-\frac{1}{6} \\\ y_3=\frac{5}{6} \\\ y_4=-\frac{5}{6}[/latex] Ответ: (-2; 1); (2; -1); (1/6; 5/6); (-1/6; -5/6)