Question

Determine the number of solutions to this system of linear equations (0, 1, infinity):
y = 7x + 8
-7x + y = -8
(1 point)
This system of linear equations has

Answer 1

To determine the number of solutions to the given system of linear equations, we can analyze the equations:

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

We can manipulate the second equation to compare it with the first equation. Let's rearrange the second equation:

Starting with:
\[
-7x + y = -8
\]

Add \( 7x \) to both sides:
\[
y = 7x - 8
\]

Now we have two equations:
1. \( y = 7x + 8 \)
2. \( y = 7x - 8 \)

Next, we can set the right sides of the equations equal to each other to check for intersections:
\[
7x + 8 = 7x - 8
\]

Subtract \( 7x \) from both sides:
\[
8 = -8
\]

This is a contradiction, which means the two lines represented by the equations are parallel and will never intersect. Since they are parallel, there is no solution to the system of equations.

Thus, the answer is:

**This system of linear equations has 0 solutions.**