1. **State the problem:** We are given the system of linear equations: $$6x - 2y = 10$$ $$y = 3x - 5$$ We need to determine which statement about the system is true: whether it has one solution, no solutions, or infinitely many solutions. 2. **Rewrite the first equation to compare with the second:** Start with the first equation: $$6x - 2y = 10$$ Isolate $y$: $$-2y = 10 - 6x$$ Divide both sides by $-2$: $$y = \frac{10 - 6x}{-2}$$ Show the cancellation step: $$y = \frac{\cancel{10} - 6x}{\cancel{-2}} = -5 + 3x$$ So, $$y = 3x - 5$$ 3. **Compare with the second equation:** The second equation is: $$y = 3x - 5$$ Both equations represent the same line. 4. **Conclusion:** Since both equations represent the same line, the system has infinitely many solutions (all points on the line). **Final answer:** The system has infinitely many solutions.