Question

{7х+5у=12. {4х+у=18 способом прибавления​ Смотреть ответ aniabondar aniabondar

Answer 1

To solve the system of equations using the method of addition (also known as the method of elimination), we need to eliminate one of the variables by adding the two equations together. Let's go step-by-step:

Given system of equations:

1. 7x + 5y = 12
2. 4x + y = 18

Step 1: Multiply the second equation by 5 to make the coefficients of y in both equations equal (5y in the first equation and -5y in the second equation):

2. 4x + y = 18 5 * (4x + y) = 5 * 18 20x + 5y = 90

Step 2: Now, add the two equations together to eliminate y:

(7x + 5y) + (20x + 5y) = 12 + 90 27x + 10y = 102

Step 3: Solve the obtained equation for one variable (preferably x or y). Let's solve for x:

27x = 102 - 10y x = (102 - 10y) / 27

Step 4: Substitute the value of x into one of the original equations to solve for y. Let's use equation 1:

7x + 5y = 12 7((102 - 10y) / 27) + 5y = 12

Step 5: Solve for y:

Multiply the entire equation by 27 to eliminate the fraction:

7(102 - 10y) + 135y = 27 * 12 714 - 70y + 135y = 324 714 + 65y = 324

Step 6: Now, solve for y:

65y = 324 - 714 65y = -390 y = -390 / 65 y = -6

Step 7: Finally, substitute the value of y back into one of the original equations to solve for x. Let's use equation 1:

7x + 5y = 12 7x + 5(-6) = 12 7x - 30 = 12 7x = 12 + 30 7x = 42 x = 42 / 7 x = 6

So, the solution to the system of equations is x = 6 and y = -6.