1. **State the problem:** Solve the system of equations for $y$ given: $$2x + y = 8$$ $$2x - y = 12$$ and $x = 7$. 2. **Substitute $x = 7$ into both equations:** $$2(7) + y = 8$$ $$2(7) - y = 12$$ which simplifies to: $$14 + y = 8$$ $$14 - y = 12$$ 3. **Solve the first equation for $y$:** $$y = 8 - 14$$ $$y = -6$$ 4. **Solve the second equation for $y$:** $$14 - y = 12$$ $$- y = 12 - 14$$ $$- y = -2$$ $$y = 2$$ 5. **Check for consistency:** The two values for $y$ are different ($-6$ and $2$), which means the system is inconsistent with $x=7$. 6. **Conclusion:** There is no value of $y$ that satisfies both equations simultaneously when $x=7$. The system has no solution for $y$ at $x=7$.