x²-12xy +36y²=36x+6y=8 

x²-12xy +36y²=36

x+6y=8

Ответ:

(X - 6*Y)² = 36

X + 6*Y = 8

Получаем две системы

Х - 6 * Y = 6                        X - 6 * Y = -6

X + 6 * Y = 8                        X + 6 * Y = 8

X₁ = 7    Y₁ = 1/6                 X₂ = 1   Y₂ = 7/6

Ответ #2:

x²-12xy +36y²=36x+6y=8

x²-12xy +36y²=36

x=8-6y

(8-6y)²-12(8-6y)y+36y²=36

64-96y+36y²-96y+72y²+36y²=36

144y²-192y+28=0

36y²-48y+7=0

Δ=(-48)²-4*36*7

Δ=2304-1008

Δ=1296

Δ=36

y₁=(-(-48)-36)/(2*36)

y₁=12/72

y₁=1/6

y₂=(-(-48)+36)/(2*36)

y₂=84/72

y₂=7/6

x₁=8-6*1/6

x₁=8-1

x₁=7

x₂=8-6*7/6

x₂=8-7

x₂=1

Источник: https://znanija.com/task/262184