Question

How many solutions does this system have?

2x + y = 3
6x = 9 – 3y
(1 point)
Responses

one

none

infinite

two
Answer
are you sure
Answer
are you sure?
Answered by GPT 3.5
The system has one solution.
Answered by GPT 3.5
Apologies for the confusion in my previous response. Let's solve the system of equations to determine the number of solutions.

2x + y = 3 ........... (equation 1)
6x = 9 – 3y ......... (equation 2)

Let's solve equation 2 for y:
6x = 9 – 3y
3y = 9 - 6x
y = (9 - 6x) / 3
y = 3 - 2x ..........(equation 3)

Since equation 1 and equation 3 both represent the same line (2x + y = 3 and y = 3 - 2x), the system of equations is dependent. This means that there are infinitely many solutions.

Therefore, the correct answer is infinite.
Answered by GPT 3.5
Apologies for the confusion once again. Let's re-evaluate the system of equations:

2x + y = 3 ........... (equation 1)
6x = 9 – 3y ......... (equation 2)

Let's solve equation 2 for y:
6x = 9 – 3y
3y = 9 - 6x
y = (9 - 6x) / 3
y = 3 - 2x ..........(equation 3)

Now we have equation 1 (2x + y = 3) and equation 3 (y = 3 - 2x).

We can substitute equation 3 into equation 1 to solve for x:
2x + (3 - 2x) = 3
2x + 3 - 2x = 3
3 = 3

The equation 3 = 3 is always true, which suggests that the two equations are representing the same line. Therefore, the system of equations has infinitely many solutions.

So, the correct answer is infinite.