1. The problem asks for the number of solutions to the system of linear equations: $$y = -5x + 3$$ $$y = -5x - 3$$ 2. Both equations are in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, both lines have the same slope $m = -5$ but different y-intercepts: $3$ and $-3$. 4. Lines with the same slope but different y-intercepts are parallel and never intersect. 5. Since the lines do not intersect, there are no points $(x,y)$ that satisfy both equations simultaneously. 6. Therefore, the system has \textbf{no solutions}. Final answer: \textbf{no solutions}