А)
{x + y = 7
{x² + xy + y² = 43
{x² + 2xy + y² = 49
{x² + xy + y² = 43
{x + y = 7
{xy = 6
{x = 7 - y
{(7-y)y = 6
{x = 7-y
{y² - 7y + 6 = 0
D = 49 - 24 = 25
y₁ = (7-5)/2 = 1
x₁ = 7-1 = 6
y₂ = (7+5)/2 = 6
x₂ = 7-6 = 1
Ответ: (1; 6); (6; 1)
в)
{x = 3 - y
{9 - 6y + y² - y² - 4(3-y)y + 11 = 0
{x = 3 - y
{4y² - 18y + 20 = 0 => 2y² - 9y + 10 = 0
D = 81 - 80 = 1
y₁ = (9 - 1)/4 = 2
x₁ = 3 - 2 = 1
y₂ = (9+1)/4 = 2,5
x₂ = 3 - 2,5 = 0,5
Ответ: (0,5; 2,5); (1; 2)