Question

How many solutions does the system of equations have?

8x−6y=48
8x+6y=48 (1 point)
Responses

one
one

none
none

infinite
infinite

two

Answer 1

[AI-generated answer — Bot GPT 3.5]

one

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the number of solutions in the system of equations, we can solve them simultaneously.

The given system of equations is:
8x - 6y = 48 (Equation 1)
8x + 6y = 48 (Equation 2)

Notice that both equations have the same coefficients for both x and y, but the sign of the y-term is different. This indicates that the lines represented by these equations are parallel.

Since parallel lines never intersect, the system of equations has no solution (none).

Therefore, the correct response is: none.

Answer 3

[AI-generated answer — Explain Bot]

To determine how many solutions the system of equations has, we need to solve the equations and see how many points of intersection they have.

We have the following system of equations:
8x - 6y = 48 (Equation 1)
8x + 6y = 48 (Equation 2)

To find the solution, we can solve the system of equations by using the method of elimination:

1. Add Equation 2 to Equation 1:
(8x - 6y) + (8x + 6y) = 48 + 48
16x = 96
x = 96/16
x = 6

2. Substitute the value of x back into one of the original equations (Equation 1):
8(6) - 6y = 48
48 - 6y = 48
-6y = 0
y = 0

Therefore, the system of equations has a unique solution where x = 6 and y = 0.

So the correct response is "one" solution.