Question

y-3x=1
x^2-2xy+y^2=9
Решите систему

Answer 1

$x^{2}-2xy+y^{2}=(x+y)^{2}=9 \ x+y=3,x+y=-3$
получаем 2 подсистемы уравнений:
$left { {{y-3x=1} atop {x+y=3}} right.$ и  $left { {{y-3x=1} atop {x+y=-3}} right.$
1)  $left { {{y-3x=1} atop {x+y=3}} right. left { {{y=1+3x} atop {x+1+3x=3}} right. left { {{y=1+3x} atop {4x=2}} right. left { {{y= frac{5}{2}} atop {x=frac{1}{2}}} right.$
2)  $left { {{y-3x=1} atop {x+y=-3}} right. left { {{y=1+3x} atop {x+1+3x=-3}} right. left { {{y=1+3x} atop {4x=-4}} right. left { {{y=-2} atop {x=-1} right.$