Determine the number of solutions of this system of linear equations: x+2y=−4 ��� + 2 ��� = − 4 4x+8y=−16 4 ��� + 8 ��� = − 16 This question requires you to show your work. Responses Infinitely Many Solutions Infinitely Many Solutions - not selected, this is the correct answer No Solutions No Solutions - no response given One Solution

Answer 1

To determine the number of solutions, we can see if the two equations are equivalent or if they are inconsistent.

First, let's see if the second equation is a multiple of the first equation:

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

This means that the second equation is actually just a multiple of the first equation. Therefore, these two equations represent the same line and have infinitely many solutions. The correct answer is: Infinitely Many Solutions.