Question

2x-8y=7 -2x+7y=5 розв'язати систему методом додавання.

Answer 1

Ответ:

Объяснение:

      { 2x-8y=7

(+)   {-2x+7y=5

---------------------.

-y=-12   (podstawiam do (1)równania : 2x-8y=7

2x-8*(-12)=7

2x+96=7

2x=7-96

2x=-89  // : (2)

x= -89/2=  -44,5

OTBET:rozwiazaniem układu równań jest para liczb: (-44,5 ; -12)

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination), you need to add the two equations in a way that eliminates one variable. Here's how you can do it step by step:

Given system of equations:

1. 2x - 8y = 7
2. -2x + 7y = 5

Step 1: Multiply the second equation by 4 to make the x terms cancel out when added together. 4(-2x + 7y) = 4(5) -8x + 28y = 20

Step 2: Now, add the two equations together. (2x - 8y) + (-8x + 28y) = 7 + 20 2x - 8y - 8x + 28y = 27

Step 3: Combine like terms. -6x + 20y = 27

Step 4: Divide through by the common coefficient of y, which is 20, to solve for y. (20y)/20 = 27/20 y = 27/20

Step 5: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation for this. 2x - 8(27/20) = 7 2x - 27/10 = 7

Step 6: Solve for x. 2x = 7 + 27/10 2x = 70/10 + 27/10 2x = (70 + 27)/10 2x = 97/10

x = (97/10) / 2 x = 97/10 * 1/2 x = 97/20

Step 7: The solution to the system of equations is x = 97/20 and y = 27/20.