1. **Stating the problem:** We have two shopping bags with prices and quantities of two types of compotes: A (abóbora) and M (morango). Bag 1: 3A + 2M = 17 Bag 2: 4A + 1M = 16 We want to find the prices of A and M, i.e., solve the system: $$\begin{cases} 3x + 2y = 17 \\ 4x + y = 16 \end{cases}$$ where $x$ is the price of compota de abóbora and $y$ is the price of compota de morango. 2. **Using substitution method:** From the second equation: $$4x + y = 16 \implies y = 16 - 4x$$ 3. **Substitute $y$ in the first equation:** $$3x + 2(16 - 4x) = 17$$ $$3x + 32 - 8x = 17$$ $$3x - 8x = 17 - 32$$ $$-5x = -15$$ 4. **Solve for $x$:** $$x = \frac{-15}{-5} = 3$$ 5. **Find $y$ using $y = 16 - 4x$:** $$y = 16 - 4(3) = 16 - 12 = 4$$ 6. **Check the solution:** Substitute $x=3$, $y=4$ into both equations: - $3(3) + 2(4) = 9 + 8 = 17$ ✓ - $4(3) + 4 = 12 + 4 = 16$ ✓ **Final answer:** $$\boxed{(x, y) = (3, 4)}$$