Question

Решить систему x+y=0 x2+y2=16

Answer 1

X+y=0
2x+2y=16
2x=16-2y(2)
x=8-y
8-y+y=0

Answer 2

We can solve this system of equations by using substitution. Solving for one of the variables in terms of the other from the first equation, and substituting into the second equation.

From the first equation, we can solve for x in terms of y:

x = -y

Substituting this into the second equation:

(-y)² + y² = 16

Simplifying:

2y² = 16

y² = 8

y = ±√8 = ±2√2

Now, we can use these values of y to solve for x using x = -y:

if y = 2√2, then x = -2√2 if y = -2√2, then x = 2√2

Therefore, the solutions to the system of equations are:

(x, y) = (-2√2, 2√2) and (2√2, -2√2)