1. **State the problem:** Solve the system of equations: $$2x + y = 8$$ $$2x - y = 12$$ 2. **Given values:** $x = 7$ and $y = 7$. 3. **Check if the given values satisfy the first equation:** $$2(7) + 7 = 14 + 7 = 21 \neq 8$$ So, the given values do not satisfy the first equation. 4. **Check if the given values satisfy the second equation:** $$2(7) - 7 = 14 - 7 = 7 \neq 12$$ So, the given values do not satisfy the second equation either. 5. **Solve the system using substitution or elimination:** Add the two equations: $$ (2x + y) + (2x - y) = 8 + 12 $$ $$ 2x + y + 2x - y = 20 $$ $$ 4x = 20 $$ 6. **Divide both sides by 4:** $$ \cancel{4}x = \frac{20}{\cancel{4}} $$ $$ x = 5 $$ 7. **Substitute $x=5$ into the first equation:** $$ 2(5) + y = 8 $$ $$ 10 + y = 8 $$ 8. **Solve for $y$:** $$ y = 8 - 10 $$ $$ y = -2 $$ 9. **Final solution:** $$ x = 5, \quad y = -2 $$ These values satisfy both equations.