1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + y = 9 \\ 3x - y = 16 \end{cases}$$ 2. **Explain the elimination method:** The goal is to eliminate one variable by adding or subtracting the equations. 3. **Add the two equations:** $$ (2x + y) + (3x - y) = 9 + 16 $$ Simplify: $$ 2x + 3x + y - y = 25 $$ $$ 5x = 25 $$ 4. **Solve for $x$:** $$ x = \frac{25}{5} = 5 $$ 5. **Substitute $x=5$ into one of the original equations, for example $2x + y = 9$:** $$ 2(5) + y = 9 $$ $$ 10 + y = 9 $$ 6. **Solve for $y$:** $$ y = 9 - 10 = -1 $$ 7. **Final solution:** $$ (x, y) = (5, -1) $$ This means the two lines intersect at the point $(5, -1)$.