1. **State the problem:** Solve the system of equations using the elimination method: $$2x + 5y = 9$$ $$2x + 3y = 7$$ 2. **Explain the elimination method:** The goal is to eliminate one variable by subtracting or adding the equations so that one variable cancels out. 3. **Subtract the second equation from the first:** $$\begin{aligned} (2x + 5y) - (2x + 3y) &= 9 - 7 \\ 2x - 2x + 5y - 3y &= 2 \\ 0 + 2y &= 2 \\ 2y &= 2 \end{aligned}$$ 4. **Solve for $y$:** $$y = \frac{2}{2} = 1$$ 5. **Substitute $y=1$ into one of the original equations to find $x$:** Using the second equation: $$2x + 3(1) = 7$$ $$2x + 3 = 7$$ $$2x = 7 - 3 = 4$$ 6. **Solve for $x$:** $$x = \frac{4}{2} = 2$$ 7. **Final answer:** $$\boxed{x=2, y=1}$$