Решите системы уравнений [latex]a) \left \{ {{ y^{2}-xy=12 } \atop {3y-x=10}} \right. b) \left \{ {{3 y^{2}-2xy=28 } \atop {x+3y=-2}} \right. [/latex]

a) [latex] \left \{ {{y^2-xy=12} \atop {3y-x=10}} \right. [/latex] [latex] \left \{ {{x=3y-10} \atop {y^2-y(3y-10)=12}} \right. [/latex] [latex] \left \{ {{x=3y-10} \atop {y^2-3y^2+10y-12=0}} \right. [/latex] [latex] \left \{ {{x=3y-10} \atop {-2y^2+10y-12=0}} \right. [/latex] [latex] \left \{ {{x=3y-10} \atop {y^2-5y+6=0}} \right. [/latex] [latex]{y^2-5y+6=0[/latex] [latex]D=(-5)^2-4*1*6=1[/latex] [latex]y_1= \frac{5+1}{2} =3,[/latex]     [latex]x_1=3*3-10=-1[/latex] [latex]y_2= \frac{5-1}{2} =2,[/latex]      [latex]x_2=3*2-10=-4[/latex] Ответ: (-1;3);  (-4;2) b) [latex] \left \{ {{3y^2-2xy=28} \atop {x+3y=-2}} \right. [/latex] [latex] \left \{ {{x=-2-3y} \atop {3y^2-2y(-2-3y)=28}} \right. [/latex] [latex] \left \{ {{x=-2-3y} \atop {3y^2+4y+6y^2-28=0}} \right. [/latex] [latex] \left \{ {{x=-2-3y} \atop {9y^2+4y-28=0}} \right. [/latex] [latex]9y^2+4y-28=0[/latex] [latex]D=4^2-4*9*(-28)=1024[/latex] [latex]y_1= \frac{-4+32}{18} = \frac{14}{9}= 1 \frac{5}{9},[/latex]     [latex]x_1=-2-3* \frac{14}{9} =-6 \frac{2}{3} [/latex] [latex]y_2= \frac{-4-32}{18} =-2,[/latex]              [latex]x_2=-2-3*(-2)=4[/latex] Ответ: [latex](-4 \frac{2}{3};1 \frac{5}{9} ) [/latex];  [latex](4;-2)[/latex]