Question

 x^{2} -у^{2} =8,
х-у=2 решите пожалуйста систему

Answer 1

$left { {{x^2-y^2=8} atop {x-y=2}} right. \ left { {{(x-y)(x+y)=8} atop {x-y=2}} right. \ left { {{2(x+y)=8} atop {x-y=2}} right. \ left { {{x+y=4} atop {x-y=2}} right. \ left { {{x=4-y} atop {4-y-y=2}} right. \ left { {{x=4-y} atop {2y=4-2}} right. \ left { {{y=1} atop {x=4-y=4-1=3}} right.$

Answer 2

$left { {{ x^{2}- y ^{2} =8} atop {x-y=2}} right. Rightarrow left { {{(x-y)(x+y)=8} atop {x-y=2}} right. Rightarrow left { {{2(x+y)=8} atop {x-y=2}} right. Rightarrow left { {{x+y=4} atop {x-y=2}} right.$

сложим два уравнение 2х=6, х=3
Найдем у из второго уравнения системы:
х-у=2,
 у=х-2=3-2=1

Ответ (3;1)