1. **State the problem:** Wendy bought 9 notebooks and 4 ballpens for 225, and Peter bought 8 notebooks and 6 ballpens for 222. We need to find the price of one notebook and one ballpen. 2. **Set variables:** Let $x$ be the price of one notebook and $y$ be the price of one ballpen. 3. **Write the system of equations:** $$9x + 4y = 225$$ $$8x + 6y = 222$$ 4. **Solve the system using elimination or substitution. Here, use elimination:** Multiply the first equation by 3 and the second by 2 to align coefficients of $y$: $$3(9x + 4y) = 3(225) \Rightarrow 27x + 12y = 675$$ $$2(8x + 6y) = 2(222) \Rightarrow 16x + 12y = 444$$ 5. **Subtract the second from the first:** $$ (27x + 12y) - (16x + 12y) = 675 - 444$$ $$ 27x - \cancel{12y} - 16x + \cancel{12y} = 231$$ $$ 11x = 231$$ 6. **Solve for $x$:** $$ x = \frac{231}{11} = 21$$ 7. **Substitute $x=21$ into the first original equation:** $$9(21) + 4y = 225$$ $$189 + 4y = 225$$ 8. **Solve for $y$:** $$4y = 225 - 189 = 36$$ $$ y = \frac{36}{4} = 9$$ **Final answer:** The price of one notebook is $21$ and the price of one ballpen is $9$.