Question

{x=y-2 x²+y²=4 решить алгебраидным способом

Answer 1

x=y-2

x^2+y^2=4

y^2-4y+4+y^2=4

2y^2-4y=0

2y(y-2)=0

y1=0

y2=2

x1=-2

x2=0

Answer 2

$\left \{ {{x=y-2} \atop {x^{2}+y^{2}}=4} \right.\\\\\left \{ {{x=y-2} \atop {(y-2)^{2}+y^{2}}=4} \right.\\\\\left \{ {{x=y-2} \atop {y^{2}-4y+4+y^{2}}=4} \right\\\\\left \{ {{2y^{2}-4y=0}\atop {x=y-2}} \right.\\\\\left \{ {{y^{2}-2y=0}\atop {x=y-2}} \right.\\\\\left \{ {{y(y-2)=0} \atop {x=y-2}} \right.\\\\\left \{ {y_{1} =0} \atop {x_{1}=- 2}} \right.\\\\\left \{ {{y_{2}= 2} \atop {x_{2}= 0}} \right.$

Ответ : (- 2 ; 0) , (0 ; 2)