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

Question

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

Answer 1

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.