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 po
Responses

Infinitely Many Solutions
Infinitely Many Solutions

One Solution
One Solution

No Solutions

Answer 1

To determine the number of solutions for the system of linear equations, we can start by analyzing the given equations:

1. **First equation**:
\[
x + 2y = -4
\]

2. **Second equation**:
\[
4x + 8y = -16
\]

Next, we can see if the second equation is a multiple of the first equation.

Multiply the first equation by 4:
\[
4(x + 2y) = 4(-4)
\]
Distributing the 4 gives:
\[
4x + 8y = -16
\]

Notice that after multiplying the first equation by 4, we end up with the second equation exactly. Therefore, the second equation does not provide any new information; it is just a scaled version of the first equation.

Since both equations represent the same line, we conclude that they have infinitely many solutions along that line.

### Conclusion:
The system of equations has **infinitely many solutions**.

Thus, the answer is:
**Infinitely Many Solutions**.