Question

Система x-3y =4, xy-7y =6​

Answer 1

$\left \{ {{x-3y=4} \atop {xy-7y=6}} \right.\\\\\left \{ {{x=3y+4} \atop {(3y+4)*y-7y=6}} \right.\\\\\left \{ {{x=3y+4} \atop {3y^{2}+4y-7y-6=0 }} \right. \\\\\left \{ {{x=3y+4} \atop {3y^{2}-3y-6=0 }} \right.\\\\\left \{ {{x=3y+4} \atop {y^{2}-y-2=0 }} \right.$

$\left \{ {{x=3y+4} \atop {\left[\begin{array}{ccc}y_{1}=2 \\y_{2}=-1-teorema.Vieta \end{array}\right }} \right.\\\\\left[\begin{array}{ccc}\left \{ {{y_{1} =2} \atop {x_{1} =3*2+4}} \right. \\\left \{ {{y_{2}=-1 } \atop {x_{2} =3*(-1)+4}} \right. \end{array}\right\\\\\left[\begin{array}{ccc}\left \{ {{x_{1}=10 } \atop {y_{1} =2}} \right. \\\left \{ {{x_{2}=1 } \atop {y_{2} =-1}} \right. \end{array}\right\\\\Otvet:\boxed{(10;2),(1;-1)}$