To determine the number of solutions to the given system of linear equations, we can analyze the two equations provided:
- \(y = 7x + 8\)
- \(-7x + y = -8\)
First, let's rewrite the second equation in a more standard form:
\[ y = 7x - 8 \]
Now we have the two equations:
- \(y = 7x + 8\)
- \(y = 7x - 8\)
Next, we can see that both equations are in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
- The first equation has a slope of \(7\) and a y-intercept of \(8\).
- The second equation also has a slope of \(7\) but a y-intercept of \(-8\).
Since both equations have the same slope (\(7\)), they are parallel lines. Since the y-intercepts are different (one at \(8\) and the other at \(-8\)), the lines will never intersect.
Because the lines are parallel and do not intersect, the system of equations has no solutions.
Thus, the number of solutions to the system of linear equations is:
0 solutions.