Question

Розв*яжіть систему x^2 + y^2 = 4
x - y = 2

Answer 1

(2;0) (0;-2)

Объяснение:

x^2 + y^2 = 4

x - y = 2

$x=2+y\\x^{2} +y^2=4\\$

$(2+y)^2+y^2=4\\4+4y+y^2+y^2=4\\2y^2+4y+4-4=0\\2y^2+4y=0\\2y(y+2)=0\\2y=0\\y=0\\y+2=0\\y=-2$

Подставим y:

$x=2+y\\x=2+0\\x=2$                  $x=2+(-2)\\x=2-2\\x=0$

Answer 2

$\left \{ {{x^{2}+y^{2} =4} \atop {x-y=2}} \right.=\left \{ {{(2+y)^{2}+y^{2} =4} \atop {x=2+y}} \right. =\left \{ {{4+4y+2y^{2} =4} \atop {x=2+y}} \right. =\left \{ {{2y^{2}+4y =4-4} \atop {x=2+y}} \right.=\left \{ {{2y(y+2)=0} \atop {x=2+y}} \right. =\left \ = \left \{ \left \{ {{2y=0} \atop {x=2+y}} \right. \atop \left \{ {{y+2=0} \atop {x=2+y}} \right. \right. = \left \{ \left \{ {{y=0} \atop {x=2}} \right. \atop \left \{ {{y=-2} \atop {x=0}} \right. } \right.$

ответ: (2;0) и (04-2)

Объяснение: