Question

Помогите пожалуйста эту решить систему x+y=1 и x^2+y^2=1

Answer 1

 x+y=1 и x^2+y^2=1
x=1-y
1-2y+y^2+y^2=1
2y^2-2y=0
y=0
x=1
y=1
x=0

Answer 2

Solving the System of Equations x + y = 1 and x^2 + y^2 = 1

To solve the system of equations x + y = 1 and x^2 + y^2 = 1, we can use substitution or elimination methods to find the values of x and y that satisfy both equations.

Let's start by using the substitution method to solve the system of equations.

Substitution Method:

We can solve the first equation for y in terms of x: y = 1 - x.

Now we can substitute this expression for y into the second equation: x^2 + (1 - x)^2 = 1.

Solving this equation will give us the values of x that satisfy both equations.

Solution:

The solutions to the system of equations are the values of x and y that satisfy both equations.

Let's solve the equation x^2 + (1 - x)^2 = 1 to find the values of x that satisfy the system of equations.

Calculating the Values of x:

Using the equation x^2 + (1 - x)^2 = 1, we can solve for x: x^2 + 1 - 2x + x^2 = 1, 2x^2 - 2x = 0, 2x(x - 1) = 0.

This equation has two solutions for x: x = 0 and x = 1.

Calculating the Values of y:

Now that we have the values of x, we can find the corresponding values of y using the equation y = 1 - x.

When x = 0, y = 1 - 0 = 1. When x = 1, y = 1 - 1 = 0.

Therefore, the solutions to the system of equations are: - When x = 0, y = 1. - When x = 1, y = 0.

These are the values of x and y that satisfy both equations in the system.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.