Question

(x² - y² = 8, x - y = 2.

Answer 1

a² - b² = (a - b)(a + b)

x² - y² = 8

x - y = 2

--

(x - y)(x + y) = 8

2(x + y) = 8

x - y = 4 и

x + y = 2

Складываем

2х = 6

x = 3

3 + y = 2

y = -1

ответ (3, -1)

Answer 2

To solve the system of equations:

1. x² - y² = 8
2. x - y = 2

We can use the method of substitution or elimination. Let's use the substitution method:

From equation 2, we can express x in terms of y as x = y + 2.

Substituting this value of x into equation 1, we get:

(y + 2)² - y² = 8

Expanding the left side:

y² + 4y + 4 - y² = 8

Simplifying:

4y + 4 = 8

Subtracting 4 from both sides:

4y = 4

Dividing both sides by 4:

y = 1

Now, substitute the value of y back into equation 2 to find x:

x - 1 = 2

Adding 1 to both sides:

x = 3

Therefore, the solution to the system of equations is x = 3 and y = 1.