Question

{ 3x+y=264 2x-5y=40 решить систему уравнений методом сложения​

Answer 1

решение на фотографии

Answer 2

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. Here's how to do it step by step:

Step 1: Write down the system of equations:

1. 3x + y = 264
2. 2x - 5y = 40

Step 2: Choose a variable to eliminate. In this case, let's eliminate the variable "y."

Step 3: Multiply both sides of the first equation by 5 and the second equation by 1 to make the coefficients of "y" the same:

1. 5(3x + y) = 5(264) -> 15x + 5y = 1320
2. 1(2x - 5y) = 1(40) -> 2x - 5y = 40

Step 4: Add the two equations together to eliminate "y":

(15x + 5y) + (2x - 5y) = 1320 + 40

Step 5: Simplify the equation:

15x + 5y + 2x - 5y = 1360

Step 6: Combine like terms:

17x = 1360

Step 7: Solve for "x":

x = 1360 / 17 x = 80

Step 8: Substitute the value of "x" into one of the original equations to solve for "y." Let's use the first equation:

3x + y = 264 3(80) + y = 264 240 + y = 264

Step 9: Solve for "y":

y = 264 - 240 y = 24

Step 10: The solution to the system of equations is:

x = 80 y = 24

So, the solution to the system of equations is x = 80 and y = 24.