Решите систему уравнений методом подстановки: а) х+у=1, ху=-1 б) х^+ху=6, х-у=4

а)

{х+у=1

{ху=-1

{x = 1 - y

{xy = - 1

{x = 1 - y

{y (1 - y) = - 1

{x = 1 - y

{y^2 - y - 1 = 0

{x = 1 - y

{y^2 - y - 1 = 0

D = 1 + 4 = 5

y1 = 1 + √5 = > x1 = - √5

y2 = 1 - √ 5 = > x2 = √5

б)

{х^2+ху=6

{х-у=4

{x^2 + xy = 6

{y = x - 4

{x^2 + x (x-4) = 6

{y = x - 4

{y = x - 4

{2x^2 - 4x - 6 = 0

{y = x - 4

{x^2 - 2x - 3 = 0

D/4 = 1 + 3 = 4

x1 = 1 + 2 = 3 = > y1 = - 1

x2 = 1 - 2 = - 1 = > y2 = - 5