1. **Problem Statement:** We are given two equations based on the cost of coffee and toast: - 7 cups of coffee + 4 pieces of toast = 655 - 5 cups of coffee + 3 pieces of toast = 475 We need to find the cost of one cup of coffee and one piece of toast. 2. **Define variables:** Let $x$ be the cost of one cup of coffee. Let $y$ be the cost of one piece of toast. 3. **Write the system of equations:** $$\begin{cases} 7x + 4y = 655 \\ 5x + 3y = 475 \end{cases}$$ 4. **Solve the system using elimination:** Multiply the first equation by 3 and the second by 4 to align coefficients of $y$: $$\begin{cases} 21x + 12y = 1965 \\ 20x + 12y = 1900 \end{cases}$$ 5. **Subtract the second equation from the first:** $$ (21x + 12y) - (20x + 12y) = 1965 - 1900 $$ $$ \cancel{21x} + \cancel{12y} - \cancel{20x} - \cancel{12y} = 65 $$ $$ x = 65 $$ 6. **Substitute $x=65$ into the second original equation:** $$ 5(65) + 3y = 475 $$ $$ 325 + 3y = 475 $$ 7. **Solve for $y$:** $$ 3y = 475 - 325 $$ $$ 3y = 150 $$ $$ y = \frac{150}{3} $$ $$ y = 50 $$ **Final answer:** Cost of one cup of coffee $x = 65$ Cost of one piece of toast $y = 50$