Question

3x - 4y = 7 x + 3y = 11​

Answer 1

Ответ:

Чтобы решить систему уравнений:

3x - 4y = 7

x + 3y = 11

Мы можем использовать метод подстановки или исключения. Здесь мы будем использовать метод подстановки.

Решите второе уравнение для x:

x + 3y = 11

x = 11 - 3y

Подставьте значение x в первое уравнение:

3x - 4y = 7

3(11 - 3y) - 4y = 7

Упростите и решите для y:

33 - 9y - 4y = 7

-13y = -26

y = 2

Подставьте значение y в любое уравнение, чтобы найти x:

x + 3y = 11

x + 3(2) = 11

x + 6 = 11

x = 5

Таким образом, решением системы уравнений является x = 5 и y = 2.

Answer 2

To solve this system of linear equations for the variables x and y, you can use either the substitution method or the elimination method. I'll use the elimination method here:

Given equations:

1. 3x - 4y = 7
2. x + 3y = 11

Let's eliminate one of the variables. We can do this by multiplying one or both equations by suitable constants to make the coefficients of x or y in both equations equal.

Let's multiply equation (2) by 3 to make the coefficients of y equal:

Original equation (2): x + 3y = 11

Now, multiply by 3: 3(x + 3y) = 3(11) 3x + 9y = 33

Now we have the equations:

1. 3x - 4y = 7
2. 3x + 9y = 33

Next, subtract equation (1) from equation (2) to eliminate x:

(3x + 9y) - (3x - 4y) = 33 - 7

This simplifies to:

3x + 9y - 3x + 4y = 26

Now, combine like terms:

13y = 26

Divide both sides by 13 to solve for y:

y = 26 / 13 y = 2

Now that we have found the value of y, we can substitute it into one of the original equations to solve for x. Let's use equation (2):

x + 3y = 11 x + 3(2) = 11 x + 6 = 11

Subtract 6 from both sides to solve for x:

x = 11 - 6 x = 5

So, the solution to the system of equations is: x = 5 y = 2