Question

X^2 + 4x+y^2 = 9 2x^2+8x+2y^2=9y Система уравнений хэлп

Answer 1

{x² + 4x + y² = 9
{2x² + 8x + 2y² = 9y

Первое уравнение умножим на (-2) и получим:  
{-2x² - 8x - 2y² = - 18
{2x² + 8x + 2y² = 9y
Сложим эти уравнения:
-2х² - 8x *- 2y² + 2x² + 8x + 2y² = -18 +9y
9у - 18 = 0
9у = 18
у = 18 : 9
у = 2
Подставим у = 2 в первое уравнение x² + 4x + y² = 9 и найдём х.
x² + 4x + 2² = 9
х² + 4х + 4 - 9 = 0
х² + 4х - 5 = 0
D = b² - 4ac
D = 4² - 4 · 1 · (-5) = 16 + 20 = 36
√D = √36 = 6
x₁ = (-4+6)/2 = 2/2 = 1
х₁ = 1
x₂ = (-4-6)/2 = -10/2 = - 5
х₂ = - 5
Ответ: (1; 2);  (-5; 2)

Answer 2

Solving the System of Equations

To solve the system of equations:

Equation 1: x^2 + 4x + y^2 = 9

Equation 2: 2x^2 + 8x + 2y^2 = 9y

we can use various methods such as substitution, elimination, or graphing. Let's use the substitution method to solve this system.

Substitution Method

1. Solve Equation 1 for x: x^2 + 4x + y^2 = 9 x^2 + 4x = 9 - y^2 x^2 + 4x - (9 - y^2) = 0

2. Solve Equation 2 for x: 2x^2 + 8x + 2y^2 = 9y 2x^2 + 8x - 9y + 2y^2 = 0

3. Substitute the expression for x from Equation 1 into Equation 2: 2(x^2 + 4x - (9 - y^2)) - 9y + 2y^2 = 0 2x^2 + 8x - 18 + 2y^2 - 9y + 2y^2 = 0 2x^2 + 8x + 4y^2 - 9y - 18 = 0

4. Simplify the equation: 2x^2 + 8x + 4y^2 - 9y - 18 = 0

Now we have a quadratic equation in terms of x and y. We can solve this equation using various methods such as factoring, completing the square, or using the quadratic formula. However, the equation provided in the question seems to be incomplete or incorrect, as it is missing some terms.

Please provide the complete and correct equations, and I'll be happy to help you solve the system of equations.