To determine the number of solutions for the given system of linear equations, let's analyze the equations:
- \( y = 7x + 8 \)
- \( -7x + y = -8 \)
We can rearrange the second equation into the form \( y = mx + b \):
Starting with: \[ -7x + y = -8 \] Adding \( 7x \) to both sides, we get: \[ y = 7x - 8 \]
Now, we can compare the two equations:
- \( y = 7x + 8 \)
- \( y = 7x - 8 \)
Both equations have the same slope (7), which means they are parallel. Since they have different y-intercepts (8 and -8), they will never intersect. Therefore, there are no solutions.
Thus, the system of linear equations has 0 solutions.