Question

ПОМОГИТЕ ОЧЕНЬ СРОЧНО, БАЛЛЫ ПРИСУТСТВУЮТ 1463. Решите системы уравнений: 1) {3x+5y=16, {2x+3y=9; 2) {9x-7y=95, {4x+y=34; 3) {3x-5y=23, {2x+3y=9; 4) {6x+5y=0, {2x+3y=-8 Смотреть ответ ок:_> ну если она еще есть =_) слушай, можно в группу мне СКУЧНАА:_) AzumiKatsuki AzumiKatsuki Ответ:Ну как то так=|Пошаговое объяснение: Спасибо всегда пожалуйста :D

Answer 1

System of Equations

Let's solve the given systems of equations step by step.

System 1: ``` 3x + 5y = 16 2x + 3y = 9 ```

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

From the second equation, we can express `x` in terms of `y`: ``` 2x = 9 - 3y x = (9 - 3y) / 2 ```

Substituting this value of `x` into the first equation, we get: ``` 3((9 - 3y) / 2) + 5y = 16 (27 - 9y) / 2 + 5y = 16 27 - 9y + 10y = 32 27 + y = 32 y = 32 - 27 y = 5 ```

Now, substituting the value of `y` back into the second equation, we can find `x`: ``` 2x + 3(5) = 9 2x + 15 = 9 2x = 9 - 15 2x = -6 x = -6 / 2 x = -3 ```

Therefore, the solution to the first system of equations is `x = -3` and `y = 5`.

System 2: ``` 9x - 7y = 95 4x + y = 34 ```

Again, we can use the method of substitution or elimination. Let's use the method of substitution.

From the second equation, we can express `y` in terms of `x`: ``` y = 34 - 4x ```

Substituting this value of `y` into the first equation, we get: ``` 9x - 7(34 - 4x) = 95 9x - 238 + 28x = 95 37x - 238 = 95 37x = 95 + 238 37x = 333 x = 333 / 37 x = 9 ```

Now, substituting the value of `x` back into the second equation, we can find `y`: ``` 4(9) + y = 34 36 + y = 34 y = 34 - 36 y = -2 ```

Therefore, the solution to the second system of equations is `x = 9` and `y = -2`.

System 3: ``` 3x - 5y = 23 2x + 3y = 9 ```

Let's use the method of elimination to solve this system.

Multiplying the first equation by 2 and the second equation by 3, we get: ``` 6x - 10y = 46 6x + 9y = 27 ```

Subtracting the second equation from the first equation, we eliminate `x`: ``` (6x - 10y) - (6x + 9y) = 46 - 27 6x - 10y - 6x - 9y = 19 -19y = 19 y = 19 / -19 y = -1 ```

Substituting the value of `y` back into the second equation, we can find `x`: ``` 2x + 3(-1) = 9 2x - 3 = 9 2x = 9 + 3 2x = 12 x = 12 / 2 x = 6 ```

Therefore, the solution to the third system of equations is `x = 6` and `y = -1`.

System 4: ``` 6x + 5y = 0 2x + 3y = -8 ```

Again, let's use the method of elimination to solve this system.

Multiplying the second equation by 3, we get: ``` 6x + 5y = 0 6x + 9y = -24 ```

Subtracting the first equation from the second equation, we eliminate `x`: ``` (6x + 9y) - (6x + 5y) = -24 - 0 6x + 9y - 6x - 5y = -24 4y = -24 y = -24 / 4 y = -6 ```

Substituting the value of `y` back into the first equation, we can find `x`: ``` 6x + 5(-6) = 0 6x - 30 = 0 6x = 30 x = 30 / 6 x = 5 ```

Therefore, the solution to the fourth system of equations is `x = 5` and `y = -6`.

I hope this helps! Let me know if you have any further questions.