1. **State the problem:** We have two systems of linear equations and need to determine the nature of their solutions (no solution, unique solution, or infinitely many solutions). 2. **System A:** $$y = 7x + 8$$ $$y = 7x + 5$$ These are two lines with the same slope ($7$) but different y-intercepts ($8$ and $5$). 3. **Rule:** If two lines have the same slope but different y-intercepts, they are parallel and do not intersect. 4. **Conclusion for System A:** No solution because the lines are parallel. 5. **System B:** $$-x - 3y = 1$$ $$x + 3y = -1$$ Rewrite the second equation: $$x + 3y = -1$$ Multiply the first equation by $-1$: $$x + 3y = -1$$ 6. **Observation:** Both equations are identical after simplification, meaning they represent the same line. 7. **Conclusion for System B:** Infinitely many solutions because both equations represent the same line. **Final answers:** - System A: The system has no solution. - System B: The system has infinitely many solutions.