Question

8x-3y=7 3x+y=9 система уранений способом сложения

Answer 1

Домножаем второе уравнение на 3, получаем:
1. 8х-3у=7
2.9х+3у=27
складываем:
8х-3у+9х+3у=27+7
17х=34
х=2
теперь подставляем х в первое уравнение, чтобы найти у:
8*2-3у=7
3у=9
у=3

Answer 2

Solution using the method of addition:

To solve the system of equations using the method of addition, we need to eliminate one variable by adding the two equations together. Let's solve the given system of equations step by step.

The given system of equations is: ``` 8x - 3y = 7 ---(1) 3x + y = 9 ---(2) ```

To eliminate the variable "y," we can multiply equation (2) by 3 and equation (1) by 1, and then add the two equations together.

Multiplying equation (2) by 3: ``` 3 * (3x + y) = 3 * 9 9x + 3y = 27 ---(3) ```

Multiplying equation (1) by 1: ``` 1 * (8x - 3y) = 1 * 7 8x - 3y = 7 ---(4) ```

Adding equations (3) and (4): ``` (9x + 3y) + (8x - 3y) = 27 + 7 17x = 34 ```

Dividing both sides of the equation by 17, we get: ``` x = 2 ```

Now, substitute the value of x into equation (2) to find the value of y: ``` 3 * 2 + y = 9 6 + y = 9 y = 3 ```

Therefore, the solution to the given system of equations is: ``` x = 2 y = 3 ```

So, the solution to the system of equations using the method of addition is x = 2 and y = 3.