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
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.