Question

Розвяжіть систему рівнянь {5х+3у=1 {15х-7у=51​ Смотреть ответ ArameMarukyan ArameMarukyan 1. x=1/5-3/5y нижний оставляем так же как дано 2. верхняя часть остаётся так как в 1. 15(1/5-3/5y)-7y=51 3. x=1/5- 3/5 × (-3) y=-3 4. x=2 y=-3 Якщо не складно, зроби мою відповідь найкращою, спасибі ;)

Answer 1

Solving the System of Equations

To solve the system of equations:

5x + 3y = 1
15x - 7y = 51

We can use the method of substitution or elimination to find the values of x and y.

Method of Substitution

1. Solve the first equation for x in terms of y: ``` 5x = 1 - 3y x = (1 - 3y) / 5 ```

2. Substitute the value of x in the second equation: ``` 15((1 - 3y) / 5) - 7y = 51 ```

3. Simplify and solve for y: ``` 3(1 - 3y) - 7y = 51 3 - 9y - 7y = 51 -16y = 48 y = -3 ```

4. Substitute the value of y back into the first equation to find x: ``` 5x + 3(-3) = 1 5x - 9 = 1 5x = 10 x = 2 ```

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

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