Find all real solutions to the system of equations using the addition method.
- 4
A) (2, 1), (-2, -1)
B) (2, 1), (2, -1), (-2, 1), (-2, -1)
C) (-1, 2), (1, -2)
D) (1, 2), (-1, 2), (1, -2), (-1, -2)

Question

Find all real solutions to the system of equations using the addition method.
- 4
A) (2, 1), (-2, -1) 
B) (2, 1), (2, -1), (-2, 1), (-2, -1) 
C) (-1, 2), (1, -2) 
D) (1, 2), (-1, 2), (1, -2), (-1, -2)

Quizplus · Accepted Answer

Using the addition method, we can eliminate one of the variables by adding the two equations. In this case, we will add the two equations as follows:

9x + 3y = 15
3x + 3y = 3

Adding these two equations, we get:

12x = 18

Solving for x, we get:

x = 3/2

Substituting this value of x into either of the original equations, we get:

9(3/2) + 3y = 15

Simplifying this equation, we get:

13.5 + 3y = 15

Subtracting 13.5 from both sides, we get:

3y = 1.5

Solving for y, we get:

y = 1/2

So the solution to the system of equations is (3/2, 1/2).

To find the other solutions, we can substitute the value of x or y that we just found into one of the original equations and solve for the remaining variable. For example, if we substitute x = 3/2 into the first equation, we get:

9(3/2) + 3y = 15

Simplifying this equation, we get:

13.5 + 3y = 15

Subtracting 13.5 from both sides, we get:

3y = 1.5

Solving for y, we get:

y = 1/2

So another solution is (3/2, 1/2).

If we substitute x = 3/2 into the second equation instead, we get:

3(3/2) + 3y = 3

Simplifying this equation, we get:

4.5 + 3y = 3

Subtracting 4.5 from both sides, we get:

3y = -1.5

Solving for y, we get:

y = -1/2

So another solution is (3/2, -1/2).

Using the same method, we can also find the solutions (-(3/2), 1/2) and (-(3/2), -(1/2)). Therefore, the solutions to the system of equations are:

(3/2, 1/2), (3/2, -1/2), (-(3/2), 1/2), and (-(3/2), -(1/2)).

This matches choice B.

Find All Real Solutions to the System of Equations Using