Question

Solve the system of equations by the addition method

x-y= -2
x+y=4
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is }. (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is {(x,y)}.
(Type an equation.)
C. There is no solution. The solution set is Ø.

Answer 1

(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).