Question

Which describes the system of equations below?

10x + 8y = –7
5x + 4y = –16

Answer 1

To analyze the system of equations, we can start by rewriting the equations for easier comparison and then use different methods to find any relationships between them.

The system is:

1. \( 10x + 8y = -7 \)
2. \( 5x + 4y = -16 \)

We can notice that the second equation is actually a scaled version of the first one. If we multiply the second equation by 2, we get:

\[
2(5x + 4y) = 2(-16)
\]
which simplifies to:

\[
10x + 8y = -32
\]

Now, we'll compare this equation with the first equation \( 10x + 8y = -7 \):

1. \( 10x + 8y = -7 \)
2. \( 10x + 8y = -32 \)

Since the left-hand sides are the same, we can set the right-hand sides equal to each other:

\[
-7 = -32
\]

This presents a contradiction, which indicates that the two equations represent parallel lines that do not intersect.

Thus, we can conclude that the system of equations has no solutions (it's inconsistent). In summary:

**The system of equations has no solution, indicating that the lines represented by the equations are parallel and do not intersect.**