Answer:
(x, y) = (1, 3)
Explanation:
You want to solve the system of equations x-y= -2; x+y=4 by the addition method.
Addition method
The addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.
Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:
(x -y) +(x +y) = (-2) +(4)
2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated
x = 1 . . . . . . divide by 2
1 +y = 4 . . . . . . . substitute for x in the second equation
y = 3 . . . . . . . . . subtract 1
The solution is (x, y) = (1, 3).