Question

Розвяжить систему методом додавання {6х-у=5 {12х+у=31​ Смотреть ответ koskakos koskakos Складываем два уравнения системы и получаем:

Answer 1

Solving the System of Equations using the Method of Addition

To solve the system of equations using the method of addition, we need to eliminate one variable by adding the two equations together. Let's solve the given system of equations step by step.

The given system of equations is: Equation 1: 6x - y = 5 Equation 2: 12x + y = 31

To eliminate the variable "y," we can add Equation 1 and Equation 2 together. Adding the left sides and the right sides separately, we get:

(6x - y) + (12x + y) = 5 + 31

Simplifying the equation, we have:

18x = 36

To find the value of "x," we divide both sides of the equation by 18:

18x/18 = 36/18 x = 2

Now that we have the value of "x," we can substitute it back into either Equation 1 or Equation 2 to find the value of "y." Let's substitute it into Equation 1:

6(2) - y = 5 12 - y = 5

To isolate "y," we subtract 12 from both sides of the equation:

- y = 5 - 12 - y = -7

Therefore, the solution to the given system of equations is x = 2 and y = -7.

Note: The solution to the system of equations was obtained by adding the two equations together to eliminate one variable. The resulting equation was then simplified and solved to find the value of the remaining variable. The obtained values were substituted back into one of the original equations to find the value of the other variable. [[1]]