1. **State the problem:** There are 23 players on a soccer team. Each player bought either a short sleeve jersey or a long sleeve jersey. A long sleeve jersey costs 50 and a short sleeve jersey costs 45. The total amount spent is 1080. We need to find how many of each jersey were purchased. 2. **Define variables:** Let $L$ be the number of long sleeve jerseys and $S$ be the number of short sleeve jerseys. 3. **Write the system of equations:** $$\begin{cases} L + S = 23 \\ 50L + 45S = 1080 \end{cases}$$ 4. **Solve the system:** From the first equation, express $S$ in terms of $L$: $$S = 23 - L$$ 5. Substitute $S$ into the second equation: $$50L + 45(23 - L) = 1080$$ 6. Distribute 45: $$50L + 1035 - 45L = 1080$$ 7. Combine like terms: $$5L + 1035 = 1080$$ 8. Subtract 1035 from both sides: $$5L = 1080 - 1035$$ $$5L = 45$$ 9. Divide both sides by 5: $$L = \frac{\cancel{5}L}{\cancel{5}} = \frac{45}{5}$$ $$L = 9$$ 10. Substitute $L = 9$ back into $S = 23 - L$: $$S = 23 - 9 = 14$$ **Final answer:** There are 9 long sleeve jerseys and 14 short sleeve jerseys purchased.