Question

Система x-3y =4, xy-7y =6​

Answer 1

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

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