Question

Which describes the system of equations below?

6x + 7y = –4
12x + 14y = –8

Answer 1

To analyze the system of equations:

1. **Identify the equations:**
- The first equation is \(6x + 7y = -4\).
- The second equation is \(12x + 14y = -8\).

2. **Determine if they are multiples of each other:**
- Notice that the second equation can be obtained by multiplying the first equation by 2.
- This can be shown as follows:
\[
2 \times (6x + 7y) = 2 \times -4
\]
This simplifies to:
\[
12x + 14y = -8
\]
- Thus, the second equation is simply a multiple of the first.

3. **Conclusion:**
- Since both equations represent the same line in a two-dimensional plane, they have **infinitely many solutions**.
- Therefore, the system of equations is dependent and consistent.

In summary, the system of equations is dependent and has infinitely many solutions.