Question

Розв'яжіть систему рівнянь способом додавання: 1) (3x+4y=-14 5x-4y = 30 2) (3x+4y = -20 (5x + 2y = -10 3) {6(x+ 2(x-4)=7y - 25 :+3) − 5(y + 2) = −11 Смотреть ответ kotugaoksana kotugaoksana Ответ:1) (3х+4у=-14 (5х-4у=30 8х=16 х=16:8 х=2 3*2+4у=-14 6+4у=-14 4у=-14-6 4у=-20 у=-20:4 у=-5 Відповідь: ( 2; -5 )2) (3х+4у=-20 (5х+2у=-10|*(-2) (3х+4у=-20 (-10х-4у=20 -7х=0 х=0 3*0+4у=-20 4у=-20 у=-5 Відповідь: ( 0; -5 )3) Я трішки не розумію де початок, а де кінець системи, можете будь ласка написати в коментарях ще раз цю систему щоб було зрозуміло, наприклад розділити із крапкою з комою, або написати з абзацу?

Answer 1

Solving the System of Equations by Addition Method

To solve the given system of equations using the addition method, we will add the two equations together in order to eliminate one of the variables. Let's go step by step:

1) Equation 1: - 3x + 4y = -14 (1)

2) Equation 2: - 5x - 4y = 30 (2)

Adding Equation 1 and Equation 2, we get:

(3x + 4y) + (5x - 4y) = -14 + 30

Simplifying the equation, we have:

8x = 16

Dividing both sides of the equation by 8, we find:

x = 2

Now, substitute the value of x into either Equation 1 or Equation 2 to find the value of y. Let's use Equation 1:

3) Equation 1 (substituting x = 2): - 3(2) + 4y = -14

Simplifying the equation, we have:

6 + 4y = -14

Subtracting 6 from both sides of the equation, we find:

4y = -20

Dividing both sides of the equation by 4, we get:

y = -5

Therefore, the solution to the given system of equations is x = 2 and y = -5.

Summary:

The solution to the system of equations is (x, y) = (2, -5).

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