1. **State the problem:** We need to graph the system of equations and determine the solution for the system: $$6x - 3y = 3$$ $$4x - 2y = 8$$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$ to graph easily.** For the first equation: $$6x - 3y = 3$$ Subtract $6x$ from both sides: $$-3y = -6x + 3$$ Divide both sides by $-3$: $$y = \frac{\cancel{-6}x}{\cancel{-3}} - \frac{3}{-3} = 2x - (-1) = 2x + 1$$ For the second equation: $$4x - 2y = 8$$ Subtract $4x$ from both sides: $$-2y = -4x + 8$$ Divide both sides by $-2$: $$y = \frac{\cancel{-4}x}{\cancel{-2}} - \frac{8}{-2} = 2x - (-4) = 2x + 4$$ 3. **Interpret the lines:** - First line: $y = 2x + 1$ - Second line: $y = 2x + 4$ Both lines have the same slope $2$ but different y-intercepts ($1$ and $4$), so they are parallel and will never intersect. 4. **Determine the solution:** Since the lines are parallel, there is **no solution** to the system (the system is inconsistent). **Final answer:** The system has no solution because the lines are parallel and do not intersect.