Question

Помогите решить : 3x-2y=8 6x+3y=9

Answer 1

Первое уравнение пока оставляем без изменений. Все числа второго уравнения делим на 3, получаем: 2х+у=3. Выделяем у= 3-2х. Подставляет это в первое уравнение вместо у. Получаем: 3х-2(3-2х)=8. Решаем: 3х-6+4х=8. Далее 7х=8+6. То есть 7х=14. Таким образом, Х=14/2=7. Подставляет значение Х равное 7 в уравнение у=3-2х. Получаем: 3-2*2=3-4=-1. Таким образом, Х=2, у=-1.

Answer 2

System of Equations

The given system of equations is: ``` 3x - 2y = 8 6x + 3y = 9 ```

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

Elimination Method

To eliminate one variable, we can multiply the first equation by 3 and the second equation by 2. This will allow us to eliminate the y variable.

Multiplying the first equation by 3: ``` 3 * (3x - 2y) = 3 * 8 9x - 6y = 24 ```

Multiplying the second equation by 2: ``` 2 * (6x + 3y) = 2 * 9 12x + 6y = 18 ```

Now, we can add the two equations together to eliminate the y variable: ``` (9x - 6y) + (12x + 6y) = 24 + 18 21x = 42 ```

Dividing both sides of the equation by 21, we get: ``` x = 2 ```

Finding y

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation: ``` 3x - 2y = 8 3 * 2 - 2y = 8 6 - 2y = 8 ```

Simplifying the equation: ``` -2y = 8 - 6 -2y = 2 ```

Dividing both sides of the equation by -2, we get: ``` y = -1 ```

Solution

Therefore, the solution to the system of equations is: ``` x = 2 y = -1 ```

Note: The solution to the system of equations is x = 2 and y = -1.