Find all real solutions to the system of equations using the addition method.
-3
A) (1, 3), (1, -3), (-1, 3), (-1, -3)
B) (2, -3), (-2, 3)
C) (1, 3), (-1, -3)
D) (2, 3), (2, -3), (-2, 3), (-2, -3)

Question

Find all real solutions to the system of equations using the addition method.
-3 
A) (1, 3), (1, -3), (-1, 3), (-1, -3) 
B) (2, -3), (-2, 3) 
C) (1, 3), (-1, -3) 
D) (2, 3), (2, -3), (-2, 3), (-2, -3)

Quizplus · Accepted Answer

Using the addition method, we can eliminate y: 
Adding the two equations, we get:

2x = 0

x = 0

Substituting x = 0 into either equation, we get:

3y = 9 or 3y = -9

y = 3 or y = -3

Therefore, the solutions are (0, 3), (0, -3), (2, 3), (2, -3), (-2, 3), and (-2, -3). 
The answer option that includes all of these solutions is D. Using the addition method (elimination), we can first eliminate y by adding the two equations together:
 
2x + 2y = 10
-2x + 2y = -2
 
Simplifying this equation, we get:
4y = 8
y = 2
 
Substituting y = 2 into one of the original equations, we get:
 
x + 2(2) = 5
x + 4 = 5
x = 1
 
Therefore, the solution to the system of equations is (1, 2). However, if we substitute y = -2 instead, we get the same value for x:
 
x + 2(-2) = 5
x - 4 = 5
x = 9
 
So another solution to the system of equations is (9, -2).
 
Finally, we can check that there are no other solutions to the system of equations. Therefore the answer is choice D: (2, 3), (2, -3), (-2, 3), (-2, -3).

Find All Real Solutions to the System of Equations Using