1. **State the problem:** We are given the system of equations: $$2x + 6 = y$$ $$4x - 2y = 6$$ We need to determine which statement about the solution to this system is true. 2. **Rewrite the equations in slope-intercept form:** The first equation is already solved for $y$: $$y = 2x + 6$$ For the second equation, solve for $y$: $$4x - 2y = 6$$ Subtract $4x$ from both sides: $$-2y = 6 - 4x$$ Divide both sides by $-2$: $$y = \frac{6 - 4x}{-2} = \frac{6}{-2} - \frac{4x}{-2} = -3 + 2x$$ 3. **Compare the two lines:** First line: $$y = 2x + 6$$ Second line: $$y = 2x - 3$$ Both lines have the same slope $2$ but different $y$-intercepts ($6$ and $-3$). 4. **Interpretation:** Lines with the same slope but different intercepts are parallel and do not intersect. 5. **Conclusion:** Since the lines are parallel and distinct, there are no solutions to the system. Therefore, the correct statement is: **D. There are no solutions because these lines are parallel to each other.**