Question

Решите систему уравнений x+y=5 x-y=7 методом алгебраического сложения

Answer 1

X + y = 5 
x - y = 7 
-------------------
x + x + y - y = 5 + 7 
2x = 12 
x = 6 

y = 5 - x = 5 - 6 = - 1 

Ответ:
(6; - 1)

Answer 2

Solving the System of Equations

To solve the system of equations using the method of algebraic addition, we'll add the two equations together to eliminate the variable "y".

The given system of equations is: - Equation 1: x + y = 5 - Equation 2: x - y = 7

To eliminate "y", we'll add Equation 1 and Equation 2:

(x + y) + (x - y) = 5 + 7

Simplifying the equation, we get:

2x = 12

Now, we can solve for "x" by dividing both sides of the equation by 2:

2x/2 = 12/2

x = 6

Now that we have the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's use Equation 1:

x + y = 5

Substituting x = 6:

6 + y = 5

Simplifying the equation, we get:

y = 5 - 6

y = -1

Therefore, the solution to the given system of equations is x = 6 and y = -1.

Answer: x = 6, y = -1