Question

Решите систему уравнений

Answer 1

Возводишь все в квадрат:
$5x^{2}+9y+16=25 4 x^{2} +9y+16=25$
Затем вычитаешь из 1 уравнения второе. Получаем:
$x^{2} =0$, значит х=0

ТОлько при х=0 система будет иметь смысл
находим у: 5*0+9у+16=25
9у=9
у=1

Answer 2

Возводим оба уравнения в квадрат
5х^2+9y+16=25 (1)
4x^2+9y+16=25 (2)
Из (1) вычитаем (2)
x^2=0,
x=0
Находим y - подставляем x в (1) уравнение
0+9y+16=25
9y=9
y=1
Ответ: (0;1)

Answer 3

Solving the System of Equations

Let's solve the system of equations provided.

The system of equations are as follows: 1. 2x - y = 7 2. x^2 - xy = 12

To solve the system of equations, we can use the substitution method or the elimination method. Let's use the substitution method to solve this system.

First, let's solve equation (1) for y: y = 2x - 7

Now, we can substitute this value of y into equation (2): x^2 - x(2x - 7) = 12

Expanding and simplifying the equation: x^2 - 2x^2 + 7x = 12 -x^2 + 7x = 12 x^2 - 7x - 12 = 0

Now, we can solve this quadratic equation to find the values of x. Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 1, b = -7, and c = -12.

Calculating the discriminant (b^2 - 4ac): D = (-7)^2 - 4*1*(-12) = 49 + 48 = 97

Now, using the quadratic formula: x = (7 ± √97) / 2

So, the solutions for x are: x = (7 + √97) / 2 and x = (7 - √97) / 2

Now that we have the values of x, we can find the corresponding values of y using the equation y = 2x - 7.

Conclusion

The solutions to the system of equations are: x = (7 + √97) / 2 and x = (7 - √97) / 2 Corresponding values of y can be found using the equation y = 2x - 7.