Question

помогите с решением системы уравнений, желательно с обьяснением​

Answer 1

........................

Answer 2

$\left \{ {{x^{2}-xy+y^{2}=7} \atop {x^{4}+x^{2}y^{2} +y^{4}=91}} \right.\\\\\\\left \{ {{x^{2}-xy+y^{2}=7} \atop {(x^{2}+y^{2})^{2}-x^{2}y^{2}=91}} \right.\\\\x^{2}+y^{2}=m\\\\xy=n\\\\\ \left \{ {{m-n=7} \atop {m^{2}-n^{2}=91}} \right.\\\\\\ :\left \{ {{(m-n)(m+n)=91} \atop {m-n=7}} \right.\\\\m+n=13\\\\+\left \{ {{m+n=13} \atop {m-n=7}} \right. \\-------\\2m=20\\\\m=10\\\\n=13-m=13-10=3\\\\\left \{ {{x^{2}+y^{2}=10} \atop {xy=3 }} \right.$

$\left \{ {{(x+y)^{2}-2xy =10} \atop {xy=3}} \right. \\\\\\\left \{ {{(x+y)^{2} =16} \atop {xy=3}} \right.\\\\\\1)\left \{ {{x+y=4} \atop {xy=3}} \right.\\\\x_{1}=1;_{2}=3\\\\y_{1}=3;y_{2}=1\\\\2)\left \{ {{x+y=-4} \atop {xy=3}} \right.\\\\x_{3}=-1;x_{4}=-3\\\\y_{3}=-3;y_{4}=-1\\\\Otvet:\boxed{(-1;-3),(-3;-1),(1;3),(3;1)}$