1. The problem gives us two lines: $$y = -5x + 2$$ and $$y = -5x + 6$$. 2. We want to find out if these lines intersect or not. 3. Both lines have the same slope, which is $$-5$$. This means they are parallel because parallel lines have the same slope. 4. Since the y-intercepts are different (2 and 6), the lines are not the same line. 5. Parallel lines never cross, so there is no solution where $$y = -5x + 2$$ equals $$y = -5x + 6$$. 6. To check, set the two equations equal: $$-5x + 2 = -5x + 6$$ 7. Subtract $$-5x$$ from both sides: $$\cancel{-5x} + 2 = \cancel{-5x} + 6$$ 8. This simplifies to: $$2 = 6$$ 9. This is not true, so there is no solution. **Final answer:** The lines are parallel and do not intersect, so there is no solution.