Question

Решите систему уравнений
{2x-2y=6}
{xy=-2}

Answer 1

2x-2y=6 |2

xy=-2

x-y=3; y=x-3

xy=-2

x(x-3)=-2

x²-3x+2=0

x₁+x₂=3; 1+2=3

x₁x₂=2; 1·2=2

x₁=1; x₂=2

Получается: 1 и 2.

Answer 2

$\displaystyle\left \{ {{2x-2y=6} \atop {xy=-2}} \right. \\\left \{ {{2x=6+2y~~~\bigg|:2} \atop {xy=-2}} \right. \\\left \{ {{x=3+y} \atop {xy=-2}} \right. \\(3+y)y=-2\\3y+y^2=-2\\3y+y^2+2=0\\y^2+3y+2=0\\D=3^2-4*1*2=9-8=1\\y_1=\dfrac{-3-1}{2} =-4:2=-2\\y_2=\dfrac{-3+1}{2} =-2:2=-1\\x=3+(-2)=3-2=1\\x=3+(-1)=3-1=2\\OTVET:(x_1;y_1;x_2;y_2)=(1;-2;2;-1).$