Question

x^2 + 2xy + y^2 -4x -4y = 45
x^2 - 2xy + y^2 - 2x +2y = 3

Answer 1

$left { {{x^2+2xy+y^2-4x-4y=45} atop {x^2-2xy+y^2-2x+2y=3}} right. ; ; ; left { {{(x+y)^2-4(x+y)=45} atop {(x-y)^2-2(x-y)=3}} right. \\t=x+y; ,; ; t^2-4t-45=0; ,; t_1=-5,; t_2=9\\p=x-y; ,; ; p^2-2p-3=0; ,; p_1=-1,; p_2=3\\ a)quadleft { {{x+y=-5} atop {x-y=-1}} right. ; left { {{2x=-6} atop {2y=-4}} right. ; left { {{x=-3} atop {y=-2}} right.$

$b)quad left { {{x+y=-5} atop {x-y=3}} right. ; left { {{2x=-2} atop {2y=-8}} right. ; left { {{x=-1} atop {y=-4}} right. \\c)quad left { {{x+y=9} atop {x-y=-1}} right. ; left { {{2x=8} atop {2y=10}} right. ; left { {{x=4} atop {y=5}} right. \\d)quad left { {{x+y=9} atop {x-y=3}} right. ; left { {{2x=12} atop {2y=6}} right. ; left { {{x=6} atop {y=3}} right. \\Otvet:;(-3,-2); ,; (-1,-4); ,; (4,5); ,; (6,3); .$