Question

Решите системы уравнений :
X+y=3
{
X^2+3xy+y^2-x-y=2

Answer 1

$left { {{x+y=3} atop {x^2+3xy+y^2-x-y=2}} right. ; left { {{x+y=3} atop {x^2+3xy+y^2-(x+y)=2}} right. ; left { {{(x+y)^2=9} atop {(x^2+2xy+y^2)+xy-3=2}} right. \\ left { {{x+y=3} atop {(x+y)^2+xy=5}} right. ; left { {{x+y=3} atop {9+xy=5}} right. ; left { {{x+y=3} atop {xy=-4}} right. ; left { {{x+y=3} atop {y=-frac{4}{x}}} right. \\x-frac{4}{x}-3=0; ; to ; ; ; x^2-3x-4=0; ; to ; ; x_1=-1,; x_2=4\\y_1=-frac{4}{-1}=4,; y_2=-frac{4}{4}=-1$

$Otvet:; ; (-1,4); ,; (4,-1); .$