Question

Решить систему уравнений
$left { {{ x^{2}-xy+ y^{2} =7} atop {x-y=1}} right.$

Answer 1

$left { {{ x^{2}-xy+ y^{2} =7} atop {x-y=1}} right.$
$left { {{(y+1)^2-y(y+1)+y^2=7} atop {x=y+1} right.$
Решим первое уравнение:
$y^2+2y+1-y^2-y+y^2=7$
$y^2+y-6=0$
$y = -3; 2$
$left { {{x=3} atop {y=2}} right.$ или $left { {{x=-2} atop {y=-3}} right.$

Ответ: (3; 2), (-2; -3)

Answer 2

$left { {{(1+y) ^{2} -y(1+y)+ y^{2} =7} atop {x=1+y}} right.$7

$left { {{1+2y+ y^{2}-y- y^{2} +y ^{2} =7 } atop {x=1+y}} right.$

$left { {{ y^{2}+y-6=0 } atop {x=1+y}} right.$
y = - 3                                  y = 2
x = 1 - 3 = - 2                       x = 1 + 2 = 3
Ответ: (- 2 ; - 3) , ( 3 , 2)