Question

Срочно помогите!!! Решите системы уравнений методом подстановки. Сколько сможете;( -------------------------------- {y=-3x { 5x+3y =12 ------------------- {x=2y+5 {2x+3y = -4 ---------------- {2x+3y=16 {3x -2y=11 ------------------ { 6(x+y)=5-(2x+y) { 3x-2y=-3y-3 ------------------- Заранее спасибо ^^

Answer 1

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Answer 2

Solving Systems of Equations by Substitution

To solve the given systems of equations using the method of substitution, we will substitute one equation into the other and solve for the variables. Let's solve each system step by step.

System 1: ``` y = -3x + 5 ---(1) 5x + 3y = 12 ---(2) ```

To solve this system, we can substitute equation (1) into equation (2) for the variable y:

5x + 3(-3x + 5) = 12

Simplifying the equation: ``` 5x - 9x + 15 = 12 -4x + 15 = 12 -4x = 12 - 15 -4x = -3 x = -3 / -4 x = 3/4 ```

Now, substitute the value of x back into equation (1) to find the value of y: ``` y = -3(3/4) + 5 y = -9/4 + 20/4 y = 11/4 ```

Therefore, the solution to System 1 is: ``` x = 3/4 y = 11/4 ```

System 2: ``` x = 2y + 5 ---(3) 2x + 3y = -4 ---(4) ```

To solve this system, we can substitute equation (3) into equation (4) for the variable x:

2(2y + 5) + 3y = -4

Simplifying the equation: ``` 4y + 10 + 3y = -4 7y + 10 = -4 7y = -4 - 10 7y = -14 y = -14 / 7 y = -2 ```

Now, substitute the value of y back into equation (3) to find the value of x: ``` x = 2(-2) + 5 x = -4 + 5 x = 1 ```

Therefore, the solution to System 2 is: ``` x = 1 y = -2 ```

System 3: ``` 6(x + y) = 5 - (2x + y) ---(5) 3x - 2y = -3y - 3 ---(6) ```

Let's simplify equation (5): ``` 6x + 6y = 5 - 2x - y 8x + 7y = 5 ```

Now, we can substitute equation (6) into the simplified equation (5) for the variable y: ``` 8x + 7(-3y - 3) = 5 ```

Simplifying the equation: ``` 8x - 21y - 21 = 5 8x - 21y = 5 + 21 8x - 21y = 26 ```

At this point, we have two equations: ``` 8x - 21y = 26 ---(7) 3x - 2y = -3y - 3 ---(8) ```

To solve this system, we can substitute equation (8) into equation (7) for the variable x: ``` 8(3y + 3) - 21y = 26 ```

Simplifying the equation: ``` 24y + 24 - 21y = 26 3y = 26 - 24 3y = 2 y = 2 / 3 ```

Now, substitute the value of y back into equation (8) to find the value of x: ``` 3x - 2(2/3) = -2(2/3) - 3 3x - 4/3 = -4/3 - 9/3 3x - 4/3 = -13/3 3x = -13/3 + 4/3 3x = -9/3 x = -9/3 / 3/3 x = -9/9 x = -1 ```

Therefore, the solution to System 3 is: ``` x = -1 y = 2/3 ```

To summarize, the solutions to the given systems of equations are as follows:

System 1: ``` x = 3/4 y = 11/4 ```

System 2: ``` x = 1 y = -2 ```

System 3: ``` x = -1 y = 2/3 ```

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