Question

Решите систему уравнений -5х+2y=20 2x-5y=-8. 3x+4y=0 2x+3y=1. 5y-6x=2 8x-3y=33. Никак не могу понять эту тему((( Пожалуйста решите три системы и если не сложно объясните как это решается) пожалуйста

Answer 1

Пример 2 
{3x+4y=02 x+3y=1Решение методом подстановки.{3x+4y=02 x+3y=1⇒{y=−34x2 x+3y=1⇒{y=−34x2 x+3(−34x)=1⇒{y=−34x−14x−1=0⇒{y=−34xx=−4⇒{y=3x=−4Ответ:(−4;3)
Пример 1 {−5x+2y=20 2x−5y=−8Решение методом подстановки.{−5x+2y=20 2x−5y=−8⇒{y=2,5x+10 2x−5y=−8⇒{y=2,5x+10 2x−5(2,5x+10)=−8⇒{y=2,5x+10−10,5x−42=0⇒{y=2,5x+10x=−4⇒{y=0x=−4Ответ:(−4;0)
Пример 3 
{5y−6x=28 x−3y=33Решение методом подстановки.{−6x+5y=28x−3y=33⇒{y=1,2x+0,48x−3y=33⇒{y=1,2x+0,48x−3(1,2x+0,4)=33⇒{y=1,2x+0,44,4x−34,2=0⇒{y=1,2x+0,4x=17122⇒{y=10711x=17122Ответ:(17122;10711)=(71722;9811)≈(7,773;9,727)

Answer 2

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. I will demonstrate how to solve the three systems of equations you provided.

# System 1:

``` -5x + 2y = 20 ---(1) 2x - 5y = -8 ---(2) ```

To solve this system, we can use the method of substitution. Let's solve equation (1) for x:

From equation (1): ``` -5x + 2y = 20 -5x = -2y + 20 x = (2y - 20) / 5 ```

Now, substitute this value of x into equation (2): ``` 2((2y - 20) / 5) - 5y = -8 (4y - 40) / 5 - 5y = -8 4y - 40 - 25y = -40 -21y = 0 y = 0 ```

Substitute the value of y back into equation (1): ``` -5x + 2(0) = 20 -5x = 20 x = -4 ```

Therefore, the solution to System 1 is x = -4 and y = 0.

# System 2:

``` 3x + 4y = 0 ---(3) 2x + 3y = 1 ---(4) ```

We can solve this system using the method of elimination. Multiply equation (3) by 2 and equation (4) by 3 to eliminate x:

6x + 8y = 0    ---(5)
6x + 9y = 3    ---(6)

Subtract equation (5) from equation (6): ``` 6x + 9y - (6x + 8y) = 3 - 0 y = 3 ```

Substitute the value of y back into equation (3): ``` 3x + 4(3) = 0 3x + 12 = 0 3x = -12 x = -4 ```

Therefore, the solution to System 2 is x = -4 and y = 3.

# System 3:

``` 5y - 6x = 2 ---(7) 8x - 3y = 33 ---(8) ```

We can solve this system using the method of substitution. Solve equation (7) for x:

From equation (7): ``` 5y - 6x = 2 -6x = -5y + 2 x = (5y - 2) / 6 ```

Now, substitute this value of x into equation (8): ``` 8((5y - 2) / 6) - 3y = 33 (40y - 16) / 6 - 3y = 33 40y - 16 - 18y = 198 22y = 214 y = 9.727 ```

Substitute the value of y back into equation (7): ``` 5(9.727) - 6x = 2 48.635 - 6x = 2 -6x = -46.635 x = 7.7725 ```

Therefore, the solution to System 3 is x = 7.7725 and y = 9.727.

Summary:

- System 1: x = -4, y = 0 - System 2: x = -4, y = 3 - System 3: x = 7.7725, y = 9.727

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