1. **State the problem:** Solve the system of equations by elimination: $$3x + y = 16$$ $$4x - y = 36$$ 2. **Add the two equations to eliminate $y$: ** $$ (3x + y) + (4x - y) = 16 + 36 $$ 3. Simplify the left side by canceling $y$: $$ 3x + \cancel{y} + 4x - \cancel{y} = 52 $$ 4. Combine like terms: $$ 7x = 52 $$ 5. Solve for $x$ by dividing both sides by 7: $$ x = \frac{52}{7} $$ 6. Substitute $x = \frac{52}{7}$ into the first equation to find $y$: $$ 3\left(\frac{52}{7}\right) + y = 16 $$ 7. Multiply: $$ \frac{156}{7} + y = 16 $$ 8. Subtract $\frac{156}{7}$ from both sides: $$ y = 16 - \frac{156}{7} $$ 9. Convert 16 to a fraction with denominator 7: $$ y = \frac{112}{7} - \frac{156}{7} $$ 10. Subtract: $$ y = \frac{112 - 156}{7} = \frac{-44}{7} $$ **Final answer:** $$ x = \frac{52}{7}, \quad y = \frac{-44}{7} $$