Question

(x² + y² = 2, x+y= 2.

Answer 1

Ответ:

надо написать y=2-x,

подставить вместо y в уравнении x²+y²=2,а затем в полученном уравнении x²+(2-х)²=2 посчитать (2-x)². Полученное квадратное уравнение поделить на два и представить как (x-1)²=0 и написать,что x=1 и в уравнении y=2-x подставить вместо x 1 и найти y.

Answer 2

To solve the system of equations:

1. x² + y² = 2
2. x + y = 2

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

From equation 2, we can solve for one variable in terms of the other: x = 2 - y

Now substitute this expression for x in equation 1: (2 - y)² + y² = 2

Expand the equation: 4 - 4y + y² + y² = 2

Combine like terms: 2y² - 4y + 2 = 0

Divide the equation by 2 to simplify: y² - 2y + 1 = 0

This equation can be factored as: (y - 1)² = 0

Taking the square root of both sides: y - 1 = 0 y = 1

Now substitute this value of y back into equation 2 to solve for x: x + 1 = 2 x = 1

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