To determine the number of solutions to the system of linear equations:
- \( y = 7x - 3 \)
- \( y = 7x + 3 \)
We can start by observing both equations. The first equation describes a line with a slope of 7 and a y-intercept of -3, while the second equation also has a slope of 7 but a y-intercept of 3.
Since both equations have the same slope (7), they are parallel lines. However, they have different y-intercepts (-3 and 3), which means they will never intersect.
When two lines are parallel and distinct, it indicates that there are no points (x, y) that satisfy both equations simultaneously.
Therefore, the system of equations has:
0 solutions.