1. **State the problem:** A coffee shop sold packages of coffee and tea on two different days. We want to find the cost per package of coffee and tea. 2. **Define variables:** Let $x$ be the cost per package of coffee. Let $y$ be the cost per package of tea. 3. **Write the system of equations based on the problem:** From the first day: $13x + 34y = 360$ From the second day: $49x + 31y = 774$ 4. **Use elimination to solve the system:** Multiply the first equation by 49 and the second by 13 to align coefficients of $x$: $$49(13x + 34y) = 49 \times 360$$ $$13(49x + 31y) = 13 \times 774$$ Which gives: $$637x + 1666y = 17640$$ $$637x + 403y = 10062$$ 5. **Subtract the second equation from the first to eliminate $x$:** $$ (637x + 1666y) - (637x + 403y) = 17640 - 10062 $$ $$ \cancel{637x} + 1666y - \cancel{637x} - 403y = 7578 $$ $$ 1263y = 7578 $$ 6. **Solve for $y$:** $$ y = \frac{7578}{1263} = 6 $$ 7. **Substitute $y=6$ into the first original equation to find $x$:** $$ 13x + 34(6) = 360 $$ $$ 13x + 204 = 360 $$ $$ 13x = 360 - 204 = 156 $$ $$ x = \frac{156}{13} = 12 $$ 8. **Answer:** Coffee costs $12$ per package and tea costs $6$ per package.