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.
(1 point)
Responses
One Solution
One Solution
Infinitely Many Solutions
Infinitely Many Solutions
No Solutions
x+2y=−4
4x+8y=−16
This question requires you to show your work.
(1 point)
Responses
One Solution
One Solution
Infinitely Many Solutions
Infinitely Many Solutions
No Solutions
Answers
There are no human answers yet.
Answered by
GPT 3.5
To determine the number of solutions, we need to first simplify the system of equations.
From the first equation, we can simplify it to x = -4 - 2y.
Substitute x in the second equation:
4(-4 - 2y) + 8y = -16
-16 - 8y + 8y = -16
-16 = -16
Since the equation simplifies to -16 = -16, this system of equations is consistent and dependent, meaning it has infinitely many solutions.
Therefore, the answer is: Infinitely Many Solutions.
From the first equation, we can simplify it to x = -4 - 2y.
Substitute x in the second equation:
4(-4 - 2y) + 8y = -16
-16 - 8y + 8y = -16
-16 = -16
Since the equation simplifies to -16 = -16, this system of equations is consistent and dependent, meaning it has infinitely many solutions.
Therefore, the answer is: Infinitely Many Solutions.
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