1. The problem asks how many solutions the system of linear equations has: $$y = 3x - 7$$ $$y = 3x + 5$$ 2. To find the number of solutions, we compare the two equations. Both have the same slope $3$ but different y-intercepts $-7$ and $5$. 3. The formula for the slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 4. Since the slopes are equal ($m_1 = m_2 = 3$) but the y-intercepts are different ($b_1 = -7$, $b_2 = 5$), the lines are parallel and never intersect. 5. Parallel lines have no points in common, so the system has no solution. Final answer: The system has \textbf{no solution}.