Question

X 2 - Xy=2y 2 - Xy = -1​

Answer 1

Складываем оба уравнения, получим:

x² - 2 * x * y + y² = 1.

Разложим по формуле квадрата разности, получим:

(x - y)² = 1,

x - y = 1,

x - y = -1.

Вычитаем из первого системного уравнения второе, получим:

x² - y² = 3.

Разложим как разность квадратов, получим:

(x - y) * (x + y) = 3.

Следовательно, получим две системы уравнений:

1. (x - y) * (x + y) = 3 и x - y = 1,

x + y = 3 и x - y = 1.

Складываем почленно:

2 * x = 4, откуда х = 2,

y = x - 1 = 2 - 1 = 1.

2. (x - y) * (x + y) = 3 и x - y = -1,

x + y = -3 и x - y = -1,

2 * x = -4,

x = -2,

y = x + 1 = -2 + 1 = -1.

Ответ: (2; 1) и (-2; -1).

Answer 2

To solve the system of equations:

1. X^2 - XY = 2Y^2
2. XY = -1

We can use the second equation to find the value of XY and then substitute it into the first equation to solve for X and Y.

Step 1: Solve for XY using equation 2. XY = -1

Step 2: Substitute XY into equation 1. X^2 - (-1) = 2Y^2 X^2 + 1 = 2Y^2

Step 3: Now, we need another equation involving X and Y to be able to solve for both variables. If there is no additional information or other equations, the system is underdetermined, meaning there are infinitely many solutions.

As it stands, the equations do not have a unique solution for X and Y. If there is any additional context or another equation available, please provide it so that we can find a specific solution. Otherwise, without additional information, the system has multiple solutions.