Question

Помогите с системой пжжж
xy+2(x−y)=10,
5xy−3(x−y)=11
​

Answer 1

$\left \{ {{xy+2(x-y)=10} \atop {5xy-3(x-y)=11}} \right.\\\\x-y=a \ ; \ xy=b\\\\\left \{ {{b+2a=10}|*(-5) \atop {5b-3a=11}} \right.\\\\+\left \{ {{-5b-10a=-50} \atop {5b-3a=11}} \right. \\-------\\-13a=-39\\\\a=3\\\\b=10-2a=10-2*3=4\\\\\\\left \{ {{x-y=3} \atop {xy=4}} \right.\\\\\left \{ {{x=3+y} \atop {(3+y)*y=4}} \right.$

$\left \{ {{x=3+y} \atop {y^{2} +3y-4=0}} \right. \\\\\left \{ {{x=3+y} \atop {\left[\begin{array}{ccc}y_{1} =-4\\y_{2}=1 \end{array}\right }} \right. \\\\\\\left[\begin{array}{ccc}\left \{ {{x_{1} =3-4=-1} \atop {y_{1}=-4 }} \right. \\\left \{ {{x_{2}=3+1=4 } \atop {y_{2}=1 }} \right. \\\end{array}\right\\\\Otvet:\boxed{(-1;4) \ , \ (4;1)}$