Question

Розвяжіть систему рівняннь {x-y=1;x^2+y^2=25 поможеть пж Смотреть ответ sofalesn sofalesn Объяснение: надеюсь что смогла чем то помочь) вроде все правильно (можешь если что отметить как лучший ответ, пожалуйста, спасибки)<3

Answer 1

It looks like you're asking for help with solving a system of equations. Let's work through it step by step.

Given System of Equations:

The system of equations to be solved is: - Equation 1: x - y = 1 - Equation 2: x^2 + y^2 = 25

Solution:

To solve this system of equations, we can use the substitution method. First, let's solve Equation 1 for x: - x = y + 1

Now, we can substitute this value of x into Equation 2: - (y + 1)^2 + y^2 = 25 - y^2 + 2y + 1 + y^2 = 25 - 2y^2 + 2y + 1 = 25 - 2y^2 + 2y - 24 = 0 - y^2 + y - 12 = 0

We can solve this quadratic equation to find the values of y. The solutions for y will then allow us to find the corresponding values of x.

Let's calculate the solutions for y using the quadratic formula: - y = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 1, b = 1, and c = -12.

Calculating the discriminant (b^2 - 4ac): - Discriminant = 1^2 - 4(1)(-12) = 1 + 48 = 49

Since the discriminant is positive, the solutions for y are real. Using the quadratic formula: - y = (-1 ± √49) / 2 - y = (-1 + 7) / 2 or y = (-1 - 7) / 2 - y = 6 / 2 or y = -8 / 2 - y = 3 or y = -4

Now that we have the values of y, we can find the corresponding values of x using the equation x = y + 1: - For y = 3, x = 3 + 1 = 4 - For y = -4, x = -4 + 1 = -3

Solutions:

Therefore, the solutions to the system of equations are: - When y = 3, x = 4 - When y = -4, x = -3

I hope this helps! Let me know if there's anything else I can assist you with.