Question

{(3x + 7y = 17) {( 5x - 9y = -13) Розв’язування систем двох лінійних рівнянь з двома змінними способом додавання\ 15 бвлов

Answer 1

Ответ: x=1     y=2.

Объяснение:

{3x+7y=17   |×9      27x+63y=153

{5x-9y=-13  |×7      35x-63y=-91

Суммируем эти уравнения:

62x=62  |÷62

x=1   ⇒

3*1+7y=17

7y=17-3

7y=14  |÷7

y=2.

Answer 2

To solve the system of linear equations using the method of addition (also known as the method of elimination), follow these steps:

Step 1: Write down the given system of equations:

1. 3x + 7y = 17
2. 5x - 9y = -13

Step 2: Multiply both sides of the equations to make the coefficients of y in both equations equal. This will allow you to eliminate one variable when you add the two equations together. In this case, you can multiply the first equation by 9 and the second equation by 7 to make the coefficients of y equal:

Multiply equation 1 by 9: 9(3x + 7y) = 9(17) 27x + 63y = 153

Multiply equation 2 by 7: 7(5x - 9y) = 7(-13) 35x - 63y = -91

The modified system becomes: 3) 27x + 63y = 153

4. 35x - 63y = -91

Step 3: Now, add the two modified equations (equations 3 and 4) together to eliminate y:

(27x + 63y) + (35x - 63y) = 153 - 91

Combine like terms:

27x + 35x + 63y - 63y = 62

Simplify:

62x = 62

Step 4: Solve for x:

x = 62 / 62

x = 1

Step 5: Substitute the value of x (x = 1) into one of the original equations to solve for y. Let's use equation 1:

3(1) + 7y = 17

3 + 7y = 17

Step 6: Solve for y:

7y = 17 - 3

7y = 14

y = 14 / 7

y = 2

Step 7: The solution to the system of linear equations is x = 1 and y = 2. Therefore, the values of x and y that satisfy both equations are x = 1 and y = 2.