Номера 5, 6, 7, 8. Ответьте хотя бы на 5 и 6

Ответ №1

$5)\; \; \left \{ {{x^2-y^2=21} \atop {x+y=-3}} \right. \; \left \{ {{(x-y)(x+y)=21} \atop {x+y=-3}} \right. \; \left \{ {{-3\cdot (x-y)=21} \atop {x+y=-3}} \right. \; \left \{ {{x-y=-7} \atop {x+y=-3}} \right. \; \oplus \; \ominus \\\\\left \{ {{2x=-10} \atop {2y=4}} \right. \; \left \{ {{x=-5} \atop {y=2}} \right. \; \; \Rightarrow \; \; \; (-5,2)$

$6)\; \; \left \{ {{x^2-xy+y^2=7} \atop {x-y=1}} \right. \; \left \{ {{(x^2-2xy+y^2)+xy=7} \atop {(x-y)^2=1}} \right. \; \left \{ {{(x-y)^2+xy=7} \atop {(x-y)^2=1}} \right. \; \left \{ {{1+xy=7} \atop {x-y=1}} \right. \\\\\left \{ {{xy=6} \atop {x-y=1}} \right. \; \left \{ {{(y+1)y=6} \atop {x=y+1}} \right. \; \left \{ {{y^2+y-6=0} \atop {x=y+1}} \right. \; \left \{ {{y_1=-3\; ,\; y_2=2} \atop {x_1=-2\; ,\; x_2=3}} \right. \; \; \Rightarrow \; \; (-2,-3)\; ,\; (3,2)$

$7)\; \; \left \{ {{(x-1)(y-1)=-2} \atop {x+y=1}} \right. \; \left \{ {{xy-x-y+1=-2} \atop {x+y=1}} \right. \; \left \{ {{xy-(x+y)=-3} \atop {x+y=1}} \right. \\\\\left \{ {{xy-1=-3} \atop {x+y=1}} \right. \; \left \{ {{xy=-2} \atop {x=1-y}} \right. \; \left \{ {{(1-y)y=-2} \atop {x=1-y}} \right. \; \left \{ {{y^2-y-2=0} \atop {x=1-y}} \right. \; \left \{ {{y_1=-1\; ,\; y_2=2} \atop {x_1=2\; ,\; x_2=-1}} \right. \; \; \Rightarrow \\\\(2,-1)\; ,\; \; (-1,2)$