Question

x²+y² = 18 xy = 9 1. Решите систему уравнений: A) (2; 4); (4; 2) B) (4; -2); (2; -4) E) (1; 4); (-4;-1) C) (8; 2); (-8; -2) in 711 D) (-3; -3); (3; 3)​

Answer 1

Ответ:

D

(-3;-3) (3;3)

${ ({y}^{2} } - 9)^{2} = 0$

Answer 2

To solve the system of equations, we'll substitute the value of xy from the second equation into the first equation.

Given: x² + y² = 18 ...(1) xy = 9 ...(2)

Substituting xy = 9 into equation (1), we get: x² + y² = 18 x(9/x) + y² = 18 9x/x + y² = 18 9 + y² = 18 y² = 18 - 9 y² = 9 y = ±√9 y = ±3

Now, we can substitute the values of y into equation (2) to solve for x.

If y = 3: xy = 9 x(3) = 9 3x = 9 x = 3

If y = -3: xy = 9 x(-3) = 9 -3x = 9 x = -3

So the solutions to the system of equations are: A) (2, 4); (4, 2) B) (4, -2); (2, -4) E) (1, 4); (-4, -1) C) (8, 2); (-8, -2) D) (-3, -3); (3, 3)

Therefore, option D) (-3, -3); (3, 3) is one of the solutions to the system of equations.