Question

Which describes the system of equations below?

x − 4y = –6
2x − 8y = –12

Answer 1

To analyze the system of equations:

1. The first equation is:
\[
x - 4y = -6
\]

2. The second equation is:
\[
2x - 8y = -12
\]

Let's manipulate the second equation to see how it relates to the first. We can divide the entire second equation by 2:

\[
\frac{2x}{2} - \frac{8y}{2} = \frac{-12}{2}
\]
This simplifies to:
\[
x - 4y = -6
\]

Now we see that the second equation is exactly the same as the first equation.

This means that the two equations represent the same line. Therefore, the system has infinitely many solutions, as every point on that line is a solution to the system.

So, to summarize, the system of equations is dependent and has infinitely many solutions.