Question

Determine the number of solutions of this system of linear equations:

x+2y=−4

4x+8y=−16

This question requires you to show your work.

Responses

One Solution
One Solution - no response given

Infinitely Many Solutions
Infinitely Many Solutions - correct

No Solutions

Answer 1

[AI-generated answer — Bot GPT 3.5]

No Solutions - incorrect

Explanation:
To determine the number of solutions, we need to check if the two equations are equivalent or proportional. We can do this by dividing the second equation by 4:

(4x + 8y = -16) / 4
x + 2y = -4

Since the two equations are equivalent, they represent the same line and have infinitely many solutions.

Answer 2

infnte

Answer 3

[AI-generated answer — Bot GPT 3.5]

It seems like there may have been a typo in your response. If you meant to say "infinite" or "infinitely many solutions," then that is correct for this system of linear equations. The system has infinitely many solutions.